Racing frames....something I can buy quickly and somewhat cheaply?

I'm afraid you won't see too many examples of what you are seeking. Not new, at the very least.

10 speeds haven't been made in at least 20 years. Even the lowest end road bikes are now at least 16 gears... but it isn't like the old days. Shifting is crisp and clean- no more "grind to find" shifting. The things probably shift better and easier than your 3 speed!

There are NO bikes made that conform to your cheap AND high quality unless you buy used... even then they can be pretty pricey.

I suggest that you concentrate your efforts on a used bike, perhaps 1997 (10 years old) or newer. There are plenty of good deals around, perhaps for $200 or less.

Try ANY of the following ---www.wheelworld.com, www.jensonusa.com, www.ebay.com ( category-SPORTING GOODS-cycling), www.bicyclebuys.com and www.cambriabike.com