I had to spend some time practicing (as you can see above) how to properly create an even patch. Following Jackie's advice, I started putting down small amounts of solder on the board and adding pieces on top of that, then melting the solder again to attached the piece I was holding with my left hand with tweezers. This technique worked quite well, since I could position at least one side properly before fixing it completely in place.

I think I still have to practice heating the solder once it's already added, because I probably stopped heating too early and the shape became very convex and spherical. There might also have been too much solder in some parts.

I wanted to test programming the board, but my soldering may have been insufficient and inaccurate as I realized. When I connected the board, the red light (in my case, orange from the drawer that said 'red LED') did turn on and stayed on consistently, but I could still not program the board due to some bad connection. I went back to double-check and re-solder the connections, and I realized that due to my technique of putting down solder first, some parts were floating a little bit. I think the technique is still quite useful, but I realize I should only put down a small amount first so that the pieces are not lifted off the board too far. I corrected any gaps and evened out some of the more convex connections, but my board would still not connect fully.