Re: front tires and their effects on wobbling at "high" speeds
If the tire isn't seated in the rim properly, yes, you'll get wheel bounce at higher speeds. I replaced my Walmart front wheel with a wider HD wheel from Husky, and the old tire just would not seat in it. I bought a new tire (Bell, also from Walmart) and it's fine.
If your tires are that old, replacing them is a good idea, especially if it's wonky.