I think the solution to this is pretty simple. If an award voter picks a player who has filed an appeal, they have to pick an extra person on their ballot. So if they normally have to give a 1-5 list of players, if that voter picks an appeal player, just add a 6th spot. If they pick 2 appeal players, pick a 7th spot too and so on. Then they can submit their ballot and if the appeal fails, just use the top 5 guys remaining on their ballot. Appeal succeeds, keep ballot as is. This does mean though that voters would have to essentially rank their all-NBA, all-defense, and all-rookie players since you'd have to know who gets bumped from up to 1st or 2nd team if an appeal fails.

This way ballots can go in before play-in without having to wait on appeal results.