I'm reviewing my current puzzle rooms, they're 22 as I write, so not a huge amount.
I'm not sure I understand why you can't randomly generate and place any of those three options.
Are these the sort of puzzle that, if the details and orders were changed a bit, would still be fun the second and third and tenth time you do them? Or are they the "aha" kind of puzzles that aren't really fun once you know the trick?
It's not that they can't be randomly generated.. they probably can and some of them partially already are. At the moment I have only 1 or 2 "aha" kind of puzzles, but I plan to add more.
The issue I see is that 10 randomly generated rooms from the same model with the same mechanic or the same layout won't differ from one another that much, their solution will be very recognizable. Maybe it'll keep the player entertained for the second or third time, but he'll eventually grow tired when he encounters it for the tenth time.
Not all puzzle rooms are like that, but the more a puzzle room is "handcrafted", requiring timing or logic or both, the less random generation is effective to lengthen its replay value.
For example the puzzle room with the hidden portal key randomly generates its position, but when you encounter it the second time you already know you have to listen to the sonar sound to locate it (ok maybe this is an "aha" kind of puzzle). Imagine when you do that 10 times.
You may think: "maybe you should remove a room that has low replay value and concentrate on creating rooms that have high replay value".. and you would be right, I guess.
This is true for more than 50% of the current puzzle rooms.
Maybe I should keep LRV puzzle rooms as boss rooms or treasure rooms, so the player sees them less frequently.