gosh people are really underestimating sheik's recovery abilities.
he got on when he could have rolled because whether you get on or roll there is always a 50/50 at worst for sheik on edgeguarding if she recovers correctly.
as for PP's problem...
honestly I think you're whining too much pp, you basically said, i want to have invuln before he gets near the stage and gimp him at low percent rather than try to wavedash to the ledge later so i have invuln at the right time and risk getting hit and having invuln at the right time to punish him. btw, i had this same conversation with fiz in NC when he complained about me going low with marth.
you basically just want a perfectly safe edgeguard on him when you have time to get the ledge with early invuln. (btw, this isn't just a problem vs sheik..other characters can do this to falco too..even marth)
however, since what you want is not an option that works but an option that is broken and covers everything with no risk, then what you're looking for is taking the ledge early and invuln firefox stall, so i guess your only hope is if someone can post proving that it's possible with falco since they already showed it's possible with fox.
i'm glad most foxes i play don't have the balls to do that 100% consistently every time when i'm marth. though i could still go high during their refresh, as can sheik, but that would mean always taking damage when coming back..
the sad thing is fox/falco with those invuln refreshes probably can have this perfect no risk world that pp wants...however, don't whine when you mess it up in tourney and lose a set.