DuckubingCuber347
Veteran
Nitpick but the swapping algorithm is not a modified Y-perm, the Y-perm is derived from the swapping sequence.If you execute the modified Y perm in OP an odd number of times, e.g., if you do it once now, you'll notice that the UL and UB edges are swapped. Thus, if you execute the modified Y perm an odd number of times in your solve, you'll need the [D' r2 U : M2] parity alg to un-swap those edges.
Why must you solve that edges first? I don't see why solving corners produces a different parity (albeit CF is probably slightly worse).