Never mind. Added this to my Makefile and all is well now:
test-with-coverage: rust-nightly
rm -rf ./coverage/*.profraw
RUSTFLAGS="-Z instrument-coverage" LLVM_PROFILE_FILE="./coverage/%p.profraw" cargo +nightly test
# The LLVM_PROFILE_FILE trick is necessary; otherwise, the
# .profraw files wind up in a last-writer-wins race which often
# (always?) results in a report showing 0% coverage.