After a month of following your suggestions, I wanted to give an update on my tank! I have stopped vacuuming the gravel and, instead, just vacuum the things that are loose on top of the gravel. I have started doing 40% water changes weekly (instead of 20-30% I had been doing). I also did A LOT of scrubbing and got most of the algae off. I've been trying to do a little bit of scrubbing every week to keep up with it and so far, it seems to be working. In just a month's time, you can see how much my frogbit has grown, when I had previously wondered if it would die off on me. Just this weekend when I did a water change, I noticed that my amazon sword has sent up a stalk thing. It hasn't done much yet (except get longer), so it will be interesting to see what it ends up doing. The die-off rate on my java fern has also slowed down tremendously! Overall, it looks like your suggestions have worked for my tank! Everything seems healthy, and I haven't had any issues with ich/fin rot recently. Thanks again for all of your input! On to the before- and after-pictures!
Edit: I almost forgot to add that I did add some water wisteria (back left corner) and some trident java fern. I also added more root tabs for the plants that needed it. In addition, I decided that, since my italian vals weren't getting very tall, I'd start using them as a "carpet" plant. I put them to the left of the amazon sword, and added a root tab or two around them... and they've gotten taller than they had in a long time! Go figure! They are also spreading like crazy!