Capture(var, Action(_)) == \E t \in S : t = var /\ Action(t) \* S is a constant set known to contain the variable var
and it does the capture/lowering I want.
Then I tried:
Capture(var, Action(_)) == \E t \in {var} : t = var /\ Action(t)
and that works too! I guess that's because the quantification happens outside the priming, and so t is a fresh, bound symbol rather than an _expression_ involving a variable.
Thanks again!