I think all the advice kind of clicked today in my mind in terms of what was going on with the washer. I picked up a new pump at the parts store today and installed it. I'm not convinced that the old pump was outright bad, but it definitely was plugged by the coins etc. preventing it from draining properly. Since one of the blades was broken off, I decided to replace it...I had to start somewhere and this made the most sense based on your advice and our problem. Ran a test load and everything works like a charm. Pump got all the water out in about 30 seconds and the washer went into its high speed spin like it should. I'm just glad I didn't go out and buy a new speed control before replacing the pump. I saved $300 and for $100 got the thing running like new!
Again, thanks for your patience with a rookie appliance DIY'er. While frustrating at times, I enjoy tinkering and learning new things...so all in all it was a good experience. Thanks again!!