I really like Lee dies, but also have no complaints with my CH4D wildcat dies.
: I would check them both out. Due to the size of the .577 cae, I believe the normal 7/8x14 are too small. The die body would be so thin, as to crack from hoop stress of trying to size the case. Thishappened in a set of .50 Sharps dies, and they're much thicker than the .577 dies would be for a standard press.
; Many standard presses have the larger hole as well, plugged with an insert for 7/8x14 threaded dies. My Lyman Press unfortunately doens't.