Your sales agreement should say they have 30 days to do a well. 

The investors must be provided a Private Placement Memorandum, subscription agreement, and operating agreement.  

I can buy a 2-4 unit with 20% down vs conventional can only buy a 2-4 INVESTMENT property with 25% down 4. there are options where DSCR loans dont repot to personal credit, helps in not having to show a bunch of paperwork or not one person in a partnership has to carry the debt5. way less paperwork to close on this loan type vs a conventional loan. we care about the income of the property you're buying and it's ability to service the debt of the property whether we use long term rents income, lease income, or air dna/bnb income.6. easily buy in partnerships, add people to your operating agreement, its as easy as that so bring partners into a deal. helps with scaling and raising capital or getting partners involved7. gift funds allowed to close on these as well, and like I said earlier, there's only a 10day seasoning period of funds with some lenders so that means you can literally have a private money lender deposit money into your account 11 days before closing, and you can use those funds to close!

I don't remember the precise words, but essentially he claimed that there was some sort of standard rental agreement applicable to the area and he could not (perhaps in reality would not) add anything to it at all, which struck me as oddly questionable.

If it’s tied directly to the lender as part of your mortgage agreement, you’d probably need to negotiate with them or refinance with a different lender who doesn’t require that restriction.However, if the restriction is part of the property deed itself and was placed by a previous owner or another party, it can be more complicated.

Review their management agreement.

In other words, two financing agreements "wrapped" together.But the goal here would be for the 2nd buyer to close all-cash (to skip the financing process), would that still work? 

Quote from @Quinn Olivarez: If I were the original seller, I would tell the bank I sold the house so that I could get the ball rolling on getting it out of this sub to agreement that is probably not enforceable in most jurisdictions.

Is there a way to transfer the loan agreement to my name or try some owner financing/selling strategy?

Sometimes, properties owned by non-profits have deed restrictions, zoning conditions, or agreements tied to their use.Tax Considerations: Non-profits often hold tax-exempt status, so you’ll need to ensure that taxes are assessed correctly once ownership transfers to you.Potential Public or Internal Scrutiny: If the transaction appears to undervalue the property or is perceived as exploiting a non-profit’s resources, it could lead to reputational risks for you or the organization.