I moved mine out when it was getting crowded, just get some hot water ready and put a little more in your water wells and quickly close it back up. That is how I do it, and it works for me. the thing is get in and out as fast as you can, pull the chicks, close it up then move babies to the brooder.
Mine is a large homemade bator made from a sink cabinet. It opens at the top. I have an old blanket hanging over it and I crawl under the blanket and pull it down over my hips and then open the bator lid. The blanket keeps the heat and moisture from escaping fast. I have even had the lights turn off on me while checking the eggs because the temps were holding so well. It has worked really well for me.
I think though that I am going to go ahead and build out my old dishwasher as an incubator and donate this one to a 4-H kid. This is because I have gastric reflux and to reach the bottom of this bator I have to be in the toe-touching position with the wall of the bator digging into my belly and fighting reflux at the same time.
That's real dedication, but it sounds like it's time for a change.
Oh no, I hope you get one soon!