Taxonomy menu - link to first node associated with term?
I figured it out; here's the solution in case anyone else needs this functionality.

Forget the Taxonomy Menu module. We'll build the functionality with a view.


Make a taxonomy term view (under Show when creating a view). 
Under Advanced, add this Relationship: Taxonomy Term - Representative Node. 
You can leave all the settings the same, but I suggest checking 'Require this
relationship' so empty terms will not get linked      
Also Under Advanced, change Use aggregation to Yes 
Add a filter for Taxonomy Vocabulary (with whatever vocab you want) 
Add a Content:Path field, exclude it from display and check 'Use absolute link' 
Add a Taxonomy Term:Name field and check Output this field as a link. For the Link Path use the Path Replacement Pattern from the Path field we just added (usually [path]).