It MIGHT be able to work.
Haha. I know that's the non-answer you weren't seeking, but if you look closely, the 81-88 Cutlass inner door panel has a slight upward kick to it up front which sort of goes along with the outer door skin kickup in the front. In fact, in your pictures, look along the top line of the inner door panel and you'll see where it kicks up slightly. The 78-80 does not have that. Now, will that still follow the 78 inner door mounting spots? I don't know 100% but if GM was being GM, I'd guess YES.
It's not that much of a kickup, but it may be enough to not exactly fit the way you want it to. Will it for sure? Who knows. I dont' know if anyone has done it, but if anyone has, they'll be able to tell you.
The lower panels are the same part number (if you include all the supersessions) from 78-88, so the length of the doors, at least inside, are the same.