First to answer your question. Yes you can move half the gravel, install half the filter, then do the other half. It's gonna make a mess of your water when ya stir up all the detritus caught in the gravel, and all that is gonna get pulled back down into the gravel as soon as the filter is operational. I'd still put the fish in a bucket before starting, and I'd vacuum the gravel and do a 50%-70% water change immediately after installation, prior to adding the fish. Make sure ya use a dechlorinator and that the temperature is correct before reintroducing the fish.
Thirty years ago, UGFs were THE filter of choice. Not so much today because there are more efficient methods. UGFs can be very efficient, especially in small tanks with a low bioload. The real problem is the amount of maintenance needed to keep 'em functioning properly. The gravel needs to be thoroughly vacuumed with each water change to prevent accumulation of detritus. If not, the detritus can clog the filter, slow flow through the gravel and filter plate, reduce the nitrifying capacity of the filter, and create anaerobic areas. That's a lot of work on a large tank. With a high bioload and messy fish, the amount of work will be even more, as this will need to be performed more often.
I have a coupla UGFs set-up on 10 gallon tanks, mainly due to poor planning on my part when I built my stands. I set them up mainly because I remember usin' UGFs as a kid and never havin' any issues. They work fine with a pair or group of nano fish in each tank, but I'd forgotten just how much work it took to keep 'em runnin' properly. I'm gonna conclude this experiment sooner or later and swap 'em out for sponge filters. Seriously, I wouldn't use a UGF
on anything larger than a 15 gallon and especially not on a tank with a heavy stocking density, such as you have.
What is your current filtration? In the long run, I suspect ya'd be happier with a good HOB
or canister filter and find it to be a lot less hassle.