North America to/from Europe award availability can be hard to come by---IF you're only thinking of doing your over the water segment via the US or Canada. One option is using cities in the Caribbean as your North American gateway cities going to/from Europe. BA flies non-stop to/from London to any number of islands that are easily reachable via AA from STL. Plenty of award availability there. Just this summer, living in STL myself like the OP, I had no trouble finding routes b/n europe & the u.s. by way of Barbados, the Caymans, the Bahamas, etc. And, whilst you could just connect from AA to BA/BA to AA there, you might as well give yourself the time to enjoy a day or two on the islands while you're at it.

I would agree with previous posts that you've got a LOT of cities to cram in a week. Sure, it's kinda' fun to see how much of Europe on can see in a short time, but you might want to a "less is more" approach of enjoying more quailty times in fewer places.