Ensure overlapping calls to verifyLoadedProviders are executed in sequence

This approach is slightly inelegant, but is straightforward and appears
to solve the problem. We have a backlog work item to convert this class
to use flows, which should allow for a much better approach.

Bug: 300671811
Test: Manually checked device
Change-Id: I0185274657739521be183155977aeece95e8ca2f