Level 1 - A Gentle Start
The first level is a great place to introduce a common technique: the paddle. By overlapping the endpoints of two metal sheets, we can force the physics engine to correct for the impossibility once game time starts. This generates force, which I use to speed the armadillo's trip down the cloth.
Landing precisely on the anchor point prevents bouncing, which would cause the dillo to leave the goal zone, and restart the 5 second fade timer. This need to stay inside the goal is a big factor in some later solutions.

Level 2 - Mind the Gap
Next is another common time-saving technique. This one is faster, but more expensive, than a paddle. A rubber sheet placed under maximum compression will expand, launching the armadillo into the air.
The armadillo has to land on the backstop inside the goal zone. Gliding in and tapping the other sheet first causes the dillo to roll up and out of the goal.

Level 3 - Void 1
With a larger budget I am able to build a more elaborate paddle, but the fundamentals are the same as in Level 1. The metal bars are used to minimize movement of the overlapping endpoints, forcing the free end of the paddle to move more to compensate. More motion, more speed!

Level 4 - Stop
The first of several levels where free-fall simply isn't good enough. The paddle sends the dillo flying out as well as down, thus avoiding friction with the cloth ramp that would eat up time.

Level 5 - Drop
Again, free-fall is too slow! With no anchor points to rely on, I am forced to draw on the inertia of many metal bars to keep the paddle's end nodes in place.
The additions to the cloth catcher are twofold. First, they add extra strength, without which the dillo would surely break through the cloth. Second, the destruction of the metal sheet upon impact absorbs some energy, preventing the dillo from rebounding too high.
Finally, a stray metal bar deflects the falling launcher, which would surely wreak havoc on the catcher.

Level 6 - Void 2
The first level with real money left over. Tweaking the catcher any further causes the paddle to break under its own forces, which causes the connected catcher to fail. Of course, where there are resources, there's a solution...

Level 7 - Weak Bridge
Reinforce the bridge with rope, launch the dillo as far as possible without wasting time hanging in the air, and build a catcher that deflects the dillo downward quickly. Simple!

Level 8 - Overhead Slide
The first of many levels where the designer's intent was clearly ignored. Why slide when you can launch?
The catcher here took a very long time to design, despite it's simple appearance. I kept designing over-budget rigid structures to minimize sway that was causing the fade timer to reset. Trial and error brought me to an elegant solution: have a free-swinging catcher come in from the opposite direction to neatly cancel the dillo's momentum.

Level 9 - Void 3
Optimizing a trajectory while aiming at a small wobbly target provides plenty of challenge here.

Level 10 - See-saw
Get the dillo on the far side of the fulcrum, then stop it. Here the stopping structure pulls double duty as weight to get the platform down in time.

Level 11 - Lob
A general rule of cheap building is to use what the designer gives you to its utmost. Being given a free rocket (or two!) is like striking gold. However, designer intent is again too slow, and I opt for compressed rubber.
The catcher has a long dangling metal plate to provide counter-momentum to reduce swing after absorbing the armadillo impact.

Level 12 - Void 4
Launch. Catch. Easy-peasy.

Level 13 - Lift
I weighted the lift down with as much material as I could, while also providing a ramp for the dillo to deflect off of. A paddle might be able to send the dillo over the top instead, but I haven't managed it yet...

Level 14 - Nudge
How about a shove, instead?

Level 15 - Void 5
Launch. Catch. The Voids are interesting when solving cheaply, but boring for a speedrun.

Level 16 - Trigger
One of my favorites! An over-zealous paddle design puts so much strain on the metal sheet that it breaks instantly, providing a clear shot at the goal zone.

Level 17 - Catapult
Who needs a slow catapult when there's money for a rubber launcher? Precisely spaced metal sheets let the armadillo come up, but get stuck on the way down. The metal sheet above is for momentum cancelling.

Level 18 - Void 6
The fastest level in my original set of runs. A triple-rubber launcher is focused on the dillo using metal sheets, and a lot of weight placed on the other side to stop it. Why so much money left over? Going beyond 3 rubber sheets didn't have any effect!

Level 19 - Golf
Pretty sure you aren't supposed to catch air with a putter. Using a driver on the green is just my style, though!

Level 20 - Scoop
Another designer's sequence - broken. This time I used timers to vaporize some hand-placed destruction tools than ended up getting in the way themselves.

Level 21 - Void 7
With an anchor node directly behind the goal, this level is vanilla as can be. Useless Voids.

Level 22 - Croquet
As played with a sledgehammer.

Level 23 - Guillotine
This one made me smile. A single rubber sheet couldn't launch the dillo far enough. Solution? Two of them, in a straight line! one pushes the other, and the first two-stage catapult is born! The tiny strip of cloth under the rubber keep the falling sheets from breaking the net.

Level 24 - Void 8
A cheaper catcher is possible, which means another bar to act as inertial ballast on the launcher, but doing so creates too much force, and the dillo snaps the rope like a thread. I am already skirting the edge of what is barely possible.

Level 25 - Motor
Launch. Deflect. Catch. Sounds almost like a void level, doesn't it?

Level 26 - Big wheel
A tiny budget here means I have to play the designer's game, but not without some optimizing!

Level 27 - Void 9
Any more weight on the launcher and it would demolish the catcher. Nowhere to place a deflection bar, and so the $100 goes unused.

Level 28 - Hill 1
Playing by the rules again. Sometimes you can't beat a free rocket. Metal bars instead of cloth keep friction to a minimum here.

Level 29 - Under and over
I hate playing by the rules! Free rockets, etc.

Level 30 - Void 10
Nothing to see here. Move along.

Level 31 - Hill 2
A little nudge to the dillo lets the rocket build up speed before becoming burdened.

Level 32 - Jump
Enough money and distance to make a rocket worthwhile here.

Level 33 - Void 11
Tired of this game yet? ;)

Level 34 - Quickly
Extremely limited budget makes this level one of the longest in the game. Oh, irony.

Level 35 - Swing 1
Like a void, only with useless stuff in the way.

Level 36 - Void 12
Two rubber cannons! I love chaining them together, but sadly this is the only time in the base game where its needed.

Level 37 - Pulley
With a bit more money I could have launched straight up, but as it is I have to follow designer intent. The destruction of the scoop turned into a really lucky break here! Pardon the pun.

Level 38 - Wall
Wall? What wall?

Level 39 - Void 13
The distance is so great here than I can rely on air resistance to send the launcher drifting off to the side... provided it isn't too heavy.

Level 40 - Rocket jump
Separating the rocket from the dillo in the catcher zone was a close shave.

Level 41 - Two steps
Double launched!

Level 42 - Void 14
A timer to vaporize the rocket minimizes the impact force, which is good because the dillo bounces around plenty in there.

Level 43 - Cascade
Go backwards, skip the level! I love doing things "incorrectly".

Level 44 - It's not Krypton Factor
Another level completely destroyed by an excessive budget. The launcher had to be positioned far from the dillo in order to give the rubber breaker time to vaporize. The timer feature has a minimum duration of 0.1 seconds, forcing the delay. In all, I'm very happy with this one. Another favorite.

Level 45 - Void 15
The longest run in the game, and with it's size, its obvious why. The anchor point above the launcher is too close to be used for a second stage, and the one the bridge is built on is too far. Thus, some old-fashioned ball rolling is in order.

Level 46 - Raise
Who needs an elegant lifting machine when you have brute force?

Level 47 - Over and under
Metal sheets set to overlap the anchor point bounce away upon timer start, slamming into the next invisible "link" in the cloth, causing it to snap. Throw in a timer to clear the debris, and it is a straight shot to the goal.

Level 48 - Void 16
The final void! Joyous day. Not much to say here, except the dillo cradle fusing to the steel catcher was a happy accident.

Level 49 - Loop
Another favorite, because of how broken the level is left. The designer intended the player to build a loop-de-loop and ride a cleverly latched rocket lift, but some falling bars change all that.

Level 50 - Swing 2
A real letdown compared to level 49, this one functions essentially like a Void level. But the dillo makes it home, safe and sound, so I shouldn't complain!