Any managing brokers in the Tacoma area that would be interested in this low volume arrangement?

That is an awesome arrangement.

It would be fine to ask them to accommodate a new arrangement if they're willing to sign a new lease with you, but this is not something you can obligate them to do if you are inheriting them from the previous landlord.

Andrea F. gave you which would be ideal (although maybe hard to find), you could also look for lease option arrangement or seller financing options to 'make your own terms', so to speak on the deal until you eventually qualify for conventional lending (lots of info online on both of those strategies and in BP community).  

After all, there'll be the little matter of your extra EXPENSES at your new living arrangement!?

I'm arranging to have a look hopefully tomorrow or the next day.

We require that utilities be transferred by the move-in date; if they haven't arranged for the utility transfer, they don't get the keys.

We do work with tenants on payment arrangements in certain circumstances to keep them out of eviction.

Even if an employee of a bank has money to loan, you still need a phone number to talk to, make arrangement to meet in public. 

I would suggest you check the landlord tenant laws for your state to find out what your regulations are.In my state we are required to provide temporary arrangements for tenant.