Is Chicago a viable airport for you? When traveling to Europe I always fly on Norwegian, but I have a few more airports I am able to choose from being on the west coast. They are a low cost airlines, meaning meals/luggage/seat assignments are extra, but if you just bring your own meal and are able to fit within the carryon restrictions (I always have been able to), but the planes are brand new and I've always enjoyed my flights.
I then buy the flights piece-mail and will usually fly in & out of a different airport in Europe to save $$ and to be able to see more. I'll admit I didn't find great prices for you in May or June but in September:
September 24 ORD-FAO $284 Faro/Algarve airport in southern Portugal, which is 2-3 hours from Jerez
Return: October 8 MAD-ORD $195 !!
If you could feasibly get to Chicago and back for $300-400, your total would be less than $900
OR, get the American Airlines card bonus & fly there to Chicago for free, you'd be at under $500!