Deadheading should definitely stop the clover from reseeding. I know you said you have limited gardening space. I think it pretty too and a big attractor to pollinating bees!
We've got a little more room here and I am trying to let it spread. We put crimson clover seed around our pond last fall to help control erosion. My dh apparently threw some extra seeds around one of peach trees and it has put out a hundred fruit, way more than usual........ I think the clover helped
And I can see how different/better it looks than the other peach tree! How's that for accidental experimenting for companion planting?
I think a bee hive is in our future