I've got a second concurrent project just about ready to go, though, so I need to find an additional contractor. 

Folks doing 506b/506c offerings can accept foreign investors via a concurrent Reg S offering.

You could do it as 5 concurrent Fannie loans which would be a pain in the  butt, however at the end of the day it would be better financing. 

We're at the precipice of running three rehab projects concurrently and haven't yet been in this situation before.  

This may be a good option, if you aren't trying to share the access of an existing realtor (most systems monitor/restrict concurrent logins).

Concurrent to that, I'm working to build a team of my own on the ground in the same markets they operate in (realtors, property managers, inspectors, etc) to see if I can match or beat the pro formas that I've received.

It's important that their attempts to move and your eviction proceedings are concurrent.  

The appraisal on the current primary would be done concurrently with the new home purchase appraisal.

....concurrent closings is actually more than double the work because you are introducing a "chicken or the egg" scenario wherein both mortgages will have conditions specifying that mortgage A can only fund if mortgage B funds, and mortgage B can only fund if mortgage A funds.

Yes thats what im looking for partner or investor to fund my project, but i dont think that i will call to self storage places to my direct concurrents and ask money from them.