Do multi-level multi-value relationships work in a view?
Am I asking this view to do something views can't do, by having
  multi-value references 2 levels deep?


Yes, to my knowledge there is no way to go 2 levels deep for this scenario. 

One possible solution, to work around this constraint, would be to use Views Field View and...

1) Create a team member view that uses the project nid as a contextual filter. 

2) Add the project nid (content id) as field to your original view so you can pass it to the views field view. 

3) In original view, add a views field, select the team member view you created in Step 1 and pass it the project nid (content id).