Not a common occurrence for sureI don't agree with the thought process that a RE broker would save you in this situation this is clearly title insurance and why you always want it..

It's not an ideal scenario...

In the apartment industry, typically $250-300 per unit per month is held by the banks in escrow, but R&M can be much higher - Utilities - Is there any common-area lighting?  

It's a very common mistake where an investor sold and bought properties and then when it's tax time they find out they didn't do the right process to actually qualify as a 1031 exchange.  

I’d be willing to bring in a private investor and negotiate lending termsThe ask: Based on the above scenario, has anyone done this before and what was the best method you found to fund the build?

This is quite common and you don't need an LLC for it. 

Not saying they are bad deal but that one party always has the the win win scenario. 

In that scenario, the rehab would cost you Zero cash and the rent went up, giving you an infinite CoC return (on the rehab work.

Many programs can be very similar between lenders, but you may find that in certain scenarios a particular options works best. 

That is common from many lenders and it will also give you more time if need be if one of the other options does not work.