Disclaimer
I did this run on a Powerpak. In case it matters for future reference, I used a ROM with checksum 4891ff6840da3f608618c100bc064bba.

SDA history
16-May-2009 - 0:16:46 (PAL) by ktwo (http://www.archive.org/details/2009-08-24-SDA_Speed_Runs/) (in the no-death category, but obsoleted by the new submission due to outdated strategies and less optimized gameplay)
11-May-2009 - 0:15:11 (PAL) by ktwo (http://www.archive.org/details/2009-08-24-SDA_Speed_Runs/)
03-Mar-2011 - 0:13:54 (PAL) by ktwo (https://ia902803.us.archive.org/14/items/2011-08-30-SDA_Speed_Runs/)

Speedrun information
For information about speedrunning The Addams Family, go to the SDA knowledge base (referred to as sdakb in my comments below):
https://kb.speeddemosarchive.com/Addams_Family_(NES)

Background
My previous run for this game was done over 10 years ago. A time when I only had access to a PAL-console. Although nothing ground-breaking has been found in this game since that run, I've been interested in putting up a time for the NTSC-version as well as improving the TAS.

When I finally got around to it, I started by working on the TAS and looking into the optimal route. While there are many item dependencies in this game, there is quite a bit of freedom given to the player in which order to visit the different areas. Looking at previous TASes and real-time speedruns, it seemed like everyone added their personal touch to the route, without there being a consensus on the most optimal one.

I already had a few ideas that I knew would shave a little time off the TAS, but as I started to spend more time with the game, more and more time saves were found. When the TAS was done, it was relatively straight-forward to work out the real-time route. The big question mark was whether Thing could be skipped or not. In theory/TAS, it's almost 6s that can be saved by not making the detour to collect Thing and the biggest time save I found over the previous TAS. However, after a bit of testing, I couldn't get this theoretic time save to work in real-time attempts. There were still many small optimizations from the TAS that I could take with me into the real-time attempts and the result is the submitted run.

Run comments
The route used in this speedrun is the violet/red route described in the sdakb. Below, I will comment on what went good/bad in this attempt and potential time saves that I either didn't get or didn't try for:

* It's theoretically faster to collect the $500 bill to the right of the house (at 0:37 in the video) than the one in Pugsley's room. However, exiting Pugsley's room in this case will be slightly slower in a real-time attempt. Overall, when testing this for a while in attempts, I consistently lost time overall and decided to abandon and go for the bill in Pugsley's room instead as that was the faster option for me.
* I did try for a while to see if I could do the TAS strat on the skeleton in the crypt (bouncing twice on its head while it's to the right of the small platform). I don't think I managed to get it even once and soon gave up the attempts. Looking at the TAS inputs, it doesn't look impossible to execute in real-time though. But the success rate seemed too low for a half second time save, even though it's early in the run.
* I can't immediately pinpoint any particular mistakes in the left landing, but I lost almost half a second to my previous pb (a 3s slower run overall). Comparing the individual rooms, it looks like most of it came from the toy room and the bathroom.
* I did not get the clip through the bannister after the left landing (at 2:30, frame-perfect trick). I considered resetting for this time save for a while, but after realizing it only saved ~0.3s, I decided against it and just considered it a bonus the attempts I got it in.
* I was low on health in the pond around the dollar bag and cheese slice (at 4:14). Normally when the life bar is completely depleated, like in this run, I die to the jellyfish above the cheese slice, but must have hit a lucky pixel this time. Anyways, had the health situation been better, I could have played that section a bit more aggressively. This attempt was still roughly on par with my average attempts in the pond though, but around a second can be saved here if everything goes perfectly. Health is often an issue in the pond and it was a bit of a roadblocker for me when doing attempts, so I'm ok just getting through it without any big time losses.
* The biggest mistake in the run happened in the kitchen, where I didn't jump after the splash screen. As a result, Gomez used the umbrella when gliding down to the entrance of the freezer (at 6:25). This cost ~0.7s. I rarely miss this trick, but it does require somewhat precise inputs and it's not the first time I messed up the execution here.
* The attic went phenomenally well. It was a gold split of around a second (although taken from a relatively small sample). The bats were behaving and no big execution mistakes. In hindsight, some of the corners could have been tightened up a little bit, but they're very small time losses in comparison to how often something goes really wrong in the attic.
* The chimney is another RNG-dependent room, where all three bats need to behave. Luckily, they cooperated this time. The small jump below the chimney (at 9:47) is something I've started doing after working on the TAS. I noticed that a small jump here often helped me get the first bat in the chimney to spawn in the right x-location. It's probably superstition and makes no difference, but thought I'd still mention why I jumped in that seemingly random spot.
* Pulling the rope to call Lurch before pushing the stool (at 10:09) saves slightly under 1.5s compared to first pushing the stool a bit to the left. The execution that follows is tricky though and my success rate is low for a trick that is that late in the run. Assuming no major breakthroughs are made, it's an obvious candidate to try and implement if someone would like to push the time lower though.
* My health was slightly low when rescuing Pugsley, so I decided to play it safe and avoid damage from the second ball (?) thrown from the window (at 10:53). This cost ~0.2s. Looking at the lifebar remaining at the end, it's difficult to say if I could have pushed on and tanked the damage, but it would have been on the edge. Considering the damage taken on the secret river and in Gomez' room can differ a bit between attempts, I'm fine with having played it safe this time.

Final thoughts
When doing attempts, I fairly early saw in my splits that a sub-11:20 (assuming timing to start after the first splash screen in the game) looked very doable. But it took a few pbs, general practice and implementing a few minor time saves until I considered 11:17 to be a realistic goal, I could potentially be happy with a 11:18 and an 11:16 seemed great, but less likely to be the end result. This goal didn't move for a while. The submitted run is a very high 11:16. Even though it contains one fairly big mistake (using the umbrella in the kitchen) and it's clear that the time can go lower, I'm satisified with this run. Unless something new is found in this game, I'm done.