I don't think I'd personally try for a realistic simulation of using lockpicks. Instead I'd go for a block sliding puzzle. At the center of the puzzle would be a circular piece which is trying to rotate, but it has 1 or more slots (lock difficulty level) into which the end of a rectangular block is stuck. The other end of the rectangular block would need to be freed by sliding the blocks around it, and the starting open space would be off in a corner or somewhere else not immediately useful. So it's more or like like those board games and phone games where cars are parked every which way in a parking lot nightmare (occasionally with some immovable support pillars added to the mix) and you're the valet who has to move them all around to get out the one the customer wants. Though, since they are not cars, you could add things like a consumable item that could simplify a lock by exploding one block (or just skip the puzzle), and blocks could be able to slide sideways if they were free along the whole side, etc.

Or, the thing you describe with one action causing two objects to rotate different amounts is something I've seen done in two or three adventure games. In that case there were several rotating pillars or rings which had to be aligned to make a picture. And there was a set of buttons or levers, most of which rotated two or three of the objects at once, including the possibility of one rotating clockwise and the other counterclockwise. So you might get something aligned by using button A 3 times, but then you'd use button B to get another piece aligned and one of the first pieces would get spun too much and now be unaligned... it's related to rubix cubes but not 3D.

The best lockpick mechanic I ever found was in skyrim, which used a chance-based system as such. It would actually give you a view of the lock itself, and you would simulate doing it as if in real life. Two picks used, you could rotate one lockpick and when you believed it to be in the right spot you would click. If it worked, it would open, if not, your pick would be damaged and you would have to try again. After enough damage, the pick breaks and you have to use another one.

Can't comment much since I actually like FO3/FONV and TES systems for lockpicking. Its just the right mix between in-character skill and player skill.

Beth sold a LOT of their games. If most people would not have liked the system, they'd have changed it (they kinda did but its more or less the same minigame with a different mask).

You could improve that with different kinds of locks (magical locks, harder locks, easier locks, maybe the lock can break if you're not gentle enough?), "real time lockpicking" (meaning that the game doesn't stops when you're lockpicking) or different kind of picks (this one can open magical locks but breaks easily, this one is strong but doesn't works for level 4 locks, etc).

Anyway, you shouldn't add too much depth to it if its not a central part of your RPG. Maybe a complex system is too tedious if the player has to pick a lock each 5min.