Thank you for your answer! I've edited the question so it asks more clearly about what makes the current floating point.

“if you're adding an N bit number and an M bit number, where N and M are different, then you better not use two's complement” -- Could you clarify a little bit? I believe it is entirely possible to sign extend a number using a 2's complement representation using its MSB, e.g. 4'b1111 will extend to 5'b11111, and 4'b0111 -> 5'b00111. Shouldn't it straightforward to add this to the existing barrel shifter within a floating point arithmetic logic?