I have had no trouble with bulbs generally and certainly not Dahlias in clay soil. Are you sure the trouble is the soils clay content? Al

Where do you live? If in the Deep South, the trouble is not the clay, it's the humidity and hot nights. The only dahlia I have grown with success is Bishop of Llandaff. That's not to say there are NO dahlias that do well here, but I don't think there are many.

As to summer bulbs. You can't go wrong with Zephyranthes and Crinums in the sun or Caladiums in the shade. (If you are in the South). Crinums and zephyrs are both beautiful and and they bloom repeatedly. Crinums require patience. They hate being disturbed, so expect at least a two year wait before they bloom. They are worth the wait.

As you're willing to improve your clay (best thing for it!) you might want to consider growing tuberous begonias for over the summer. You can start them indoors in pots until any late frosts have gone, and then plant out when the soil has warmed up.

Another couple which tolerate heavier soils are Watsonia (but may become weedy), and Eucomis. Plus Lilies of various kinds for both early and late summer displays.