A sort of hybrid solution might be to use a clamp on, but just clamped lightly, just enough to hold it in place until the epoxy resin under it sets, not hard enough to crush, or even distort the carbon fiber beneath it.
Now that I think of it, there is, on CGOAB, an extensive thread with color glossy photographs, of a guy building a carbon fiber recumbent frame. It should give you both ideas, and confidence that a DIY repair will work.