It seems to me you have three viable options at the moment.1) Non-renew. 

Then the lender will borrow you the $200k at a very high rate hoping you fail to make payments. 

You can have this contract subject to the monthly payments.

Even if you create a non-CA LLC, if you are managing the business from California, you will likely be deemed to be "doing business" in California and therefore likely subject to CA taxes.

While our initial down payment was modest, our loan to value is estimated at 71% based on current home value.

However, locally some places in PA are allowing ADU, but have restrictions that if you build one for a parent or a child, that once they leave it can NOT be rented to a non-relative. 

They offered to split the payments so I could pay half now and half in 40 days but still even $4K is a lot for me right now.  

They're written to avoid basis switching and also reflect the IRS' general discomfort with non-arms-length dealings, but they end up limiting a lot of very valuable improvements. 

The sky is the limit for these products, but they all have pros and cons (higher rate, lower terms, balloon payments, etc.).

(Max vacated rents - your monthly mortgage payment) = +/- net cashflow.