I think 1. a7 is the way to go. What was problematic for me was figuring out what a7 does than Kg7 doesn't, and I found a line where a7 matters.
1. a7 Qxa8
2. Rxf4+ Qe4
3. a8=Q Qxf4
4. Qd5#
With that in mind, and with 2. Re1 looking like it does the job after 1... Qd6, I think this is the solution.
What do you do after 1...Qe5?
I just think we should suspend judgment on Boris until we have all the facts through an inquiry, police investigation, and parliamentary commission...then we should explode him.
also,
I'd like to be called Lord Poopy His Most Gloriously Excellent.