  Precision study of few-electron, high-$Z$ ions is a privileged field for
probing high-field, bound-state quantum electrodynamics (BSQED). However, the
accuracy of such tests is plagued by nuclear uncertainties, which are often
larger than the BSQED effects under investigation. We propose an alternative
method with exotic atoms, and show that transitions may be found between
circular Rydberg states where nuclear contributions are vanishing while BSQED
effects remain large. When probed with newly available quantum sensing
detectors, these systems offer gains in sensitivity of \numrange{1}{2} orders
of magnitude, while the mean electric field in these systems largely exceeds
the Schwinger limit.
