Most any sort of bowie type with a sharpened clip seems as if it would work for you. The Randall 1-7 is a bit beyond the $400 limit, maybe if you can find a Blackjack 1-7 or 14 HALO? Cold Steel I'm sure has something that will fit the bill.
Not to be picky, but the OP mentioned "back cut" capability. While the Randall 1-7 comes with a sharpened swedge, the Blackjack 1-7 does not. I have owned both.