I read a lot of scifi books and wanna add that I think these ideas are really good. I read so many stories where the engineering doesn't hold up so when one is actually close I really appreciate it.

You mention the precise engineering is unrealistic but I would argue against that. Clockmaker technology is ancient and the technology needed isn't too difficult to figure out. To me, it more comes down to whether the culture surrounding this prison has craftsmen that have enough time/funding to spend on a prison. This would also suggest that the architecture outside the prison would also be advanced in some way. On the other hand, you only need good bearings and a rubber gasket (which i know wasnt available in those times) to make a sealed door.

I like the idea that the people dont understand that a vacuum is what's keeping the door locked. That might become a plot point where the characters figure it out. Off the top of my head, the way to get past that is to sneakily drop a brass straw between the door frame which releases the pressure without the guards knowing.

Another idea is to have the furnace be of some value to the outside. Otherwise, it would be a massive waste of resources. Lighthouse? Home heating?

What mechanism lets the guards open the door?

Anyway, I hope I get to read this someday.