Your weather sounds like the weather here... Ugh!
Yeah, slowly acclimating them to more sun is a very good idea.
And my indoor semps will usually let me know when they need a drink. I literally wait until they are showing signs of drying out and right before they start losing leaves, I'll give them a little drink.
I've also noticed that the larger the rosette (hen) is, the more susceptible they are to rot. The little chicks seem to survive in damper conditions easier, but it appears to be much more difficult to keep a large hen alive when strictly indoors.
Good luck!