If you have an outboard and don't use a plug, the bilge water level will become just about same level in tank compartment, so maintaining low bilge water level is imperative.
So you keep it plugged and periodically remove plug to check for water buildup and drain any off, then put it back.
If you have an I/O, plug must remain in place normally or otherwise compartment must remain sealed as it is now.
You can use neoprene strips, just need to fully Lifeseal it to the tank where ever it makes contact. I like neoprene - its grippy so the tank doesn't tend to want to slide around, its hard enough not to reshape itself, but soft enough to absorb any imperfections in glass against tank. Neoprene doesn't age in the bilge. I'd use 3/16in. against the bottom, 1/2 in. against the forward face, have no problem using 2 by lumber for cross braces, just make sure you let them dry a few days in sun before cutting to fit. Don't let wood or neoprene touch tank, only via caulk like lifeseal.
If your neoprene is shinny, lay it down on a piece of wood and take the belt sander with 80 grit to it, makes it renewed and grippy, clean residue with brush and denatured alcohol, do both sides.
How you wedge the side gaps and rear is up to you, foam is fast and easy, I would tend to want to cut my own wedges from 2x 4 fir on edge, and 1/8 in neoprene against tank, via full face lifeseal.
Did the tank fabricator locate full height sitiffeners/baffles inside, the same place as existing tank? I bet where the cross braces on top are located.