In general, I'm open to exploring the idea. I have an assortment of thoughts, in no particular order ...
How do we, as a club or as individuals, benefit from this? General exposure, obviously; anything else? If any of us make additional trips (see some of my following comments), would the museum pay anything for gas, time, etc?
Agree with your insurance thoughts. This is maybe the most critical consideration. We would want to thoroughly photograph the display before leaving.
January is typically low on other display events, so it's likely that things could be left there without impacting other displays.
I only have a couple custom trains, but I would not want museum staff running them. Maybe consider some stock train sets that the staff could run?
Maybe plan where 1-2 TBRR members show up and run trains for the day several times during the exhibit. We could also do presentations / workshops / etc on these days.
Maybe set up starts on a Friday, goes to 12 or 1pm Saturday, so not's quite as much of a rush. Tear down could start maybe 2-3pm on a Sunday so it doesn't go as late. The display would likely be smaller, too, so it wouldn't be as time-intensive.
The display should have some safety factors - such as, leave a half-baseplate distance (or more) around all the edges - partly to keep little fingers away from out stuff, partly to give trains a place to land without hitting the floor. Maybe minimize use of switches, and other opportunities for derailment.
What about cleaning? Whatever is on display will get dusty. Do we instruct the staff how to clean? Or do we come down periodically and do it?
I like the idea of using the same room, so that if there's a significant problem, it can just be closed off.
Next January is a long way away. Hopefully play brick will not be a problem then.