I have about 50k worth of capital and the bank is offering a rate buy down from 4.5% to 3.875% for 3.25 points.

Keep an eye on it because it demonstrates he's living on the edge and may fail to pay rent some day.I recommend you get rid of him when the lease expires.

I’ve been told that banks in TX are not able/willing to do a cash out refi on investment properties.

Chris -   some lenders  will not let a HELOC in 1st position.....so watch for this …...most lenders  will not do helocs on  investment  property only on primary residences  ( there may be some exceptions )   …..if these have 2 adjacent tax lots - you prob wont find a lender to lend one loan on both  properties  …..I would recommend  checking with the smaller banks and cedit unions in your area ( n Pierce / s King counties ) good luck

Does anyone know of banks (or if it is even possible) that would appraise a 1-4 unit rental property based on cashflow?

Can I use someone else's money (that wasn't gifted or loaned to me) for my down payment on a bank loan?  

What measures would I take moving forward" - easy, vet everyone better, that is also what I would have done differently.It shouldn't push anyone away, everyone makes mistakes, how we learn and move forward, or don't, is the difference between succeeding and failing.

They are non-banking investors looking for someplace to invest their money.

Though many in your inner circle outside of this community may think you are wasting time, energy and money on real estate because everybody knows somebody who has tried it and failed, this site holds a great support system that will help keep you focused and look at scenarios you may not see. 5.

We have clients using private banking systems to gain additional revenue on their rental property.