Contextual Filter tied to 2 relations?
A colleague and I got this figured out after I posted the question.

To clarify the original question: the situation is, you've got a view with a path with one argument (e.g. user/%/prospects, where the argument is expected to be a uid), but you need to use that argument in two different contextual filters - in my case, two different taxonomy comparisons between the selected user and the content I've viewing.  The problem is, a contextual filter only lets you reference one relation.  

The solution is to enter both contextual filters, but in the second one, in the "WHEN THE FILTER VALUE IS NOT IN THE URL" section, choose 'Provide default value', and in the type, choose (in this particular case) "User ID from URL".  Other 'from URL' types are available.  This allows you to 'share' one argument with two different contextual filters.