Natts in Chicago has an outstanding selection of mini Catts.His prices are very reasonable for blooming size plants.Very nice folks to deal with.He might just have what you are looking for.
Laelia alaorii has no definite bloom season for me. Seems heavier in summer though I suppose.
Laelia sincorana is an early summer bloomer.
Cattleya luteola is another early summer.
Cattleya aclandiae and schilleriana both bloom summer.
If you look up the hybrids of them, you'll be set. (sort of)
Encyclia tampensis is a native Florida orchid (I have a couple in pots, and a couple in trees) and they are not- here at least- in their native territory- an early summer bloomer. May through August is best here in Tampa, and mine bloom a bit late.