It's written out in the Deed of Trust/Mortgage and just follow the agreement.

The question is, is the "problem tenant" violating state or local law or the lease agreement? 

May be time to TERMINATE the listing agreement and hire another agent...

If the original lease is:1) Still accurate on all other issues2) Up-to date - there have been no statute changesThen you can just execute an extension agreement.

The first approved applicant is offered the rental and I give them 24 hours to pay the deposit and sign the agreement.

Yes its called a participation agreement but they all need to be in alignment and agreement.The other option is to raise is through syndication which gets a lot more expensive setup then each investor would be pari passu but would be easier for investors to agree to these terms than doing a participation agreement. 

The tenants paid by money order, presumably according to the lease agreement, and delivered payment to you, presumably according to the lease agreement. 

Is it feasible to obtain a loan or a good old boy agreement where a lender offers 100% financing for both the purchase price and construction costs at hard money rates, secured by a second position on the borrower's other properties?

You need a clearly written partnership agreement that spells everything out.

It also is helpful to have a California LLC in case you ever sell that property and move into another state so that you do not need to form a new LLC altogether with new operating agreement, just re-register in the new state as a new foreign LLC.