Thanks for the replies.
Mostly, I was just thinking that running it diagonally would give me a larger surface area, and therefore allow me to have a higher flow rate (gallons/minute) while still keeping the water velocity through the mattenfilter in the acceptable range (5-10 cm/minute, i think?).
I think I also thought I could get away without installing bracing/inserts, since the corners of the tank would serve to hold the mattenfilter in place, but as Hoppy pointed out (thanks), without substrate, I'd need to put something along the bottom, otherwise the water would probably channel underneath.
Actually, running the mattenfilter across the length of the aquarium didn't occur to me.
Thanks again for the replies and input