It's been a while! Good news: every single unaffected shrimp survived following my emergency water change, and they had all been doing VERY well until one recently got stuck in a molt. He is dying

I have purchased a new tank for these guys, and was wondering how best to make the transition. It's an all-glass 2.5 gallon (not much of an upgrade, I know, but it fits in the tiny space and is totally gorgeous). I am buying finer sand-like substrate, so the shrimp won't get "stuck" in the cracks between my larger gravel, although I suspect this only happens when shrimp are already dying and are spasming/too weak to get out.
How do I cycle this/best make the transition? Ideally, I would like to put the fine sand on top of the established larger gravel I already have, that is full of good bacteria. I guess I could move all the shrimp and their water into a clean bowl temporarily, dump the old gravel into the new tank, cover it with the new sand gravel, fill it with clean water, then let it sit for a couple of weeks? Meanwhile, I could transfer the shrimp and their rocks back into the gravel-less old tank until the new one settles.
If I am using the old water and established gravel, do I still have to wait? If so, how long? I don't have a whole lot of space to work with, and having 2 tanks around will be a bit of a challenge.