@Travis Kurtz , as @Paul G. points out, the mortgage companies like each mortgage to be secured by the collateral of that property (only).  

I would expect an fha underwriter do that exact thing, the value of the collateral is 107000

Some require additional collateral some don't.

What do you bring to the table (experience, cash, other collateral, high wage w-2 job, big IRA/401K balance, etc)? 

My partners who are very wealthy do this.. ..I borrow from banks at 5 to 6%  that's is the best you can do.. unless as stated you use your securities as collateral.. then for sure .. the loans are 1 over prime or 1 over libor.. take your pick

The collateral pledge is simply your percentage of ownership.

If the the borrower has property in California, how can it be used to collateralize the loan in case of non-payment to off-set the risk of Ohio being a foreclosure state?

"Cash" offer with a private lender only works with a cash closing i.e. no collateral.

I currently own a rental property also in Atlanta that I would like to use as collateral for the financing of this new home.

That is to cash in hand.However, if you look to seller financing as a solution to your next purchase, you can give the seller a collateral interest in your other property.