Playing the Near-Expert

My opponent in this, my 26th rated USCF game, was by far the highest-rated I'd faced.  Mark Paetz was rated 1998, nearly an expert, while I was still only rated 1519.  When you play someone rated nearly 500 points higher than you, it's exciting.  At least for me, I relish the challenge.  And of course as far as your rating goes there's almost nothing to lose and a lot to gain.

So I ended up losing, but I played decently, perhaps having some drawing chances near the end.

Here are some key positions from the game:

Here, after 53. Rxa4, I think my best move might be Bc1.  Can I hold on for the draw then?

Instead, I played 53. ... Kf5, leading to this position:

Here, I think Ke4 gives me my best chance of drawing.  Maybe some day I'll play it out against a computer.