I don't think you need that big of a sump.
I have a heavily stocked African tank.. It's a 300 gallon. The sump is built into the tank.. roughly 6" wide. There's about 10 gallons of bio balls in there. The sponge prefilters need to be rinsed out about once a week, but that's more than adequate bio-filtration.. I don't think you need a 360 gallon sump (I don't remember the exact measurements)..
If the wife doesn't want a sump, consider walling off part off the tank and doing an in-tank sump.. I really like mine. Much simplier set up.. the water falls over the overflow, over the media.. Two pumps send the water back..