White can draw, but not with 1. Bxe7.
I honestly don't understand your solution at all. How are you going to pull off a draw like that?
The draw is very simple and intuitive. White's first three moves can create stalemate, no matter what black plays: 1. Be1 h2 2. Ba5 h1Q 3. b4 ...and stalemate follows on move four.
But try solving the puzzle i send in the forum "daily puzzle submission " by MattHelfst.
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