Thanks for the feedback.
On the respawning, it is an intended mechanic that the agents will respawn in the event of a tie, and Larry does have a text that explains that but if you enter Larry's interaction range and then exit again that will trigger whether you saw the dialogue or not, so it is rather a feature of a very poorly designed dialogue system. I did try to fix that but did not manage and implementing a proper fix for the dialogue system would require too much work due to how much of the game is built around it.
For the special game, I had found the bug you mention regarding choosing Natasha or Larry, and have had a fix for that and verified that it worked correctly, what happened at one point was that one of the intermediate releases was baked with some old code due to some temporary files that the engine generates as you work on a game and those somehow got baked into the game, meaning the bugs were present, I had thought that I fixed that though, I will check and verify that. One thing you can try is I had experienced that the second time you play the special game you couldn't pick Natasha, but you could if you tried the first time. If you want to try that you can try open the game and click 3 times in the bottom left corner of the window and that should cheat to unlock the special game immediately.
The door to open is accessible if you verse Natasha in the special game (if you are not able to choose Natasha then probably the variables are wrong and it won't work). To access that door you need to stand at the pallet left of the door and jump, you will get a ping to let you know the door opened. In hindsight maybe that extra requirement didn't make sense. There is a little red light if you look up in that direction but that is most likely way too subtle and also it takes a bit to get there anyways so most likely redundant.