Puzzles aren't everyone's cup of tea.
But who doesn't like
death traps?
What's your secret to running and especially improvising death traps? Don't make me suck it out of your brain cause...er, my brain sucker death trap sucks. I mean it doesn't. *sob*
No, no! Play to your strengths. What you do is lock me in a room where the only ways out are to spill my secrets or solve a fiendish puzzle ... Wait a second ...
Think of a death trap as its own little side adventure/side trek. It's a closed loop, because if you aren't trapped in it and having to deal with it, it isn't much of a death trap. And in your case, you can include a puzzle as way to short cut out of it--just don't make it too obvious at first, and don't make it the only way out.
Then you need things for most everyone to do--if only run around like cockatrice with their heads cut off, looking for secret doors. And you need a time pressure that is obvious. You need a theme that holds it all together--like water flooding. Some kind of gas is good, too. Then finally, you need to go full gonzo. I don't much see the point in deliberately designing a "death trap" any other way. It practically conjures images of Adam West Batman. If it turns into something more like a boulder chasing Professor Jones because the players get nervous--well, that was still a gonzo death trap, even if Jones running left him little time for campy dialogue.
As for improvising, I do two basic things:
1. I'm on the alert for things that aren't death traps now, but might turn into them depending on player actions. Water flooding is really easy this way. The key is to not get to set on having a death trap. For example, I had an underground dungeon that the party explored which, if certain doors were opened, flooded parts of it. This stirred up some of the denizens, who then opened up their own secondary passages to avoid the water. In a way, the whole place was one giant death trap, if the party wasn't a bit careful. But it was also possible to navigate it and never feel that pressure. The likely result is the one I got--a couple of times, the party got mixed up in other traps/features/fights that were made into death traps by the water.
2. Once you have an idea for how something is turning into a death trap, stop a second and visualize it. Make a few guesses about what people will do. Then include elements to make those activities interesting. Remember the garbage pit in the first Star Wars. Closing walls are trite. Closing walls with garbage concealing some creature that runs, not so much.