I have a SFR property under contract to purchase in an LLC.  

.-  I'd be looking at a conventional loan (possibly owner contract) with 25% down.  

You could look more into a Lease Purchase or Land Contract instead where you are doing a seller carry scenario of sorts, then you could re-rent the property and ultimately re-sell the property. 

It appears that the property has some relation to a reservation since the Bureau of Indian Affairs is involved, plus it may be that it was purchased on a Contract for Deed, and the deed never got recorded after the property was paid for. 

How to wholesale Real Estate and flip contracts, etc.

I am in the market for an attorney or Title company with experience in dealing with contract review and wholesale (quick) closings.

As long as it's legal, of course.

If you purchase a property and inherit the tenants, tenants who most likely paid security deposits at one point, how is the legal transfer of the security deposit money handled?

And I have 3 more under progress as well as one under contract.

What you expected is irrelevant, the only thing that matters is what your purchase contract states.Normally you would demand a prorated rent, no deductions, as well as any and all deposits the tenants have paid.