In regards to closing costs, I should have said "closing costs & prepaids" - but either way this is money I have paid out of pocket already for my single family primary residence, and money I will have to pay out of pocket when purchasing the multi.The root of what I am trying to accomplish is trying to use the capital I have "stuck" in my single family I.L.O saving and waiting or using another creative financing avenue.

You would probably be obligated to mitigate your damages after evicting her, which would mean finding a replacement tenant, giving the evicted tenant grounds to demand a refund of her prepaid rent.

I have some funds in a couple different 1031 exchanges.  I have a piece of land under option, that I have been working with the City on a lot split and plans for construction of SFHs.  Let's say my purchase price is 4...

Point is, though, that title fees, recording fees, and prepaids will mostly be the same.

We will receive the refundable portion of the deposits as well as any pre-paid rent.

Landlords would take large deposits or prepaid rent if there is no credit history due to being new here.

My other prospective tenant is willing to pay a double security deposit (prepaid rent) because his credit is week. 

Loan fees, appraisal fee, lawyer fee, inspection, land survey, title survey, title lender policy, prepaid escrow item.

I would say no because 1) she doesn't report her income (not a good sign) and 2) if you feel a larger deposit or extra prepaid rent above what you would normally require, it would seem that you are already expecting her to be a liability - which usually, they will be. 

Also note if you do a VA IRRL (or any refi for that matter), there will still be closing costs and prepaid costs to process the refi.