Long story short...there's a scavenger hunt I'm participating in where I need to beat a chess.com 2000+ computer with 1. A4 2.H4.  Any thoughts on how to progress in the opening to minimize my disadvantage?

Well, there is a lot of theory to go over on this opening. I'd suggest getting some background first with Lasker's Manual of A4H4, otherwise you will be lost. Then you can go with Seirawan's Winning Chess with A4H4 and Dvoretsky's Secrets of A4H4, to get a quick overview of modern theory in this line.

how about with the basics of e5 and d5 pawns??