I suspect that part of the problem is getting my hands and feet to work at different speeds. I tend to want to treadle really quickly,
You hit the nail on the head, young Padawan. This is a problem that I struggled with at first, and I'm sure many others as well. You need to get used to sloooowwwww feet until your hands catch up. It's hard to remember, but just keep repeating to yourself, "slow feet, fast hands, slow feet, fast hands!"
There is another way to salvage overspun yarn, (even though it's TOTALLY CHEATING, it will save you from having to ply): After you're done overspinning the whole yarn, attach it to a new bobbin and run it back through the wheel in the opposite direction. Set your wheel for a fast intake so that it sucks the yarn through relatively quickly and it should leave you with a less-twisted single. Just make sure you keep an eye on it and don't let it take out too much or it will break.