I doubt finishing the mask will make a difference. Inspecting your screenshots, I'd definitely say you made the mask right, and adding a few white areas on the right shouldn't make a difference.
The problem sure does seem to be the tileset. Could you please upload the actual file for the tileset you made so we can see your transparency?
As for right now, I'm stumped. I was about to suggest that maybe the problem is that you have some completely clear tiles (since that doesn't work in KS), but then I tested putting completely clear tiles in my game and it still worked fine.
(Come to think of it, the clear tile error in KS is probably by design, anyways; just there to protect us from accidentally using them in our levels)
EDIT: By the way, your tileset is working for me (not looking corrupt), but everything is rock solid as you said; the stuff that should be in the background is solid, despite a seemingly fine mask.
I've attached my version of your tileset.