You may borrow an additional $35000 for hard cost improvements.

No co-owners/borrowers.

Getting the loan in your LLC doesn't change your borrowability.

The rental income is approximately $4,000 per month, but every bank I’ve spoken to only allows me to borrow up to $300,000 against the property.

HUD 4000.1 (I believe) is the latest HUD handbook and it goes over all requirements for originating the loan, including but not limited to occupancy requirements and exemptions.FHA occupancy : "At least one Borrower must occupy the Property within 60 Days of signing the security instrument and intend to continue occupancy for at least one year."

If the loan is not getting paid, you foreclose and sell the property to get your money back.The only other way you could get yourself in trouble is by giving the borrower cash before the work is done.  

(most hard money loans require 10-15% down depending on the split between purchase price and rehab). but that is both (1) risky and (2) expensive, as you're paying interest every month on 100% of the borrowed funds. private money is fine, you're just bearing a lot of risk and also involving the relationship in your very first deal. 

. - Hence why all the DSR loans we've seen have a required document the borrower signs that states the lender will start foreclosure proceeedings if the borrower ever occupies the property.Please correct me if I'm wrong or clarify anything I missed.

I suspect you spoke to bank employees who weren’t in their commercial lending division and didn’t understand your borrowing request. 

Or you can sell it, split the equity, and go separate ways.I'm not a fan of borrowing from family/friends unless all parties are honest and everything is documented in a written contract.