Your situation may differ and I would use all your same criteria (on all parties) and exercise extreme caution....if you are building a pool of applicants, the couple with no documented income would not likely be at the top for me (not sure what the the commission only single salary gig would be, but probably not a front runner in my pools or even meeting minimum criteria)....and you still have to even verify the third party payer would be credit worthy and even interested....

Back during the Great Recession, credit lines were closed/frozen for very credit worthy people.

The security deposit might be 1 or 2 months depending on the creditworthiness. 

I am going on a decade working for a large bank, and yes credit worthy borrowers get punished in downturns as the bank tightens policies.The funny thing is banks seem to never learn from the past.  

Is there a lender who'd issue a signature-loan type LOC, based just on my credit worthiness?

We have been generating good cash flow, but we have been try to re-position the tenant base with more credit worthy tenants and it is taking a bit longer than we would like.  

You’ve meet no potential tenants, and yet some people on this post are advising you that by lowering your credit requirements some potential renter, again you’ve never met, and has never seen the property in person is going to pursue a lawsuit based on a violation of a protected class of which credit worthiness is not one.

Depending on the credit worthiness of the tenant, these investment would typically earn 6 - 12% on an all cash investment, with the possibility than good financing can increase cash on cash return.

Consideration must also be taken when the contract is for an owner financed deal where financing is based on the creditworthiness of the individual,   in this case the seller must be notified and they must agree with assigning the contract.

It could be that the very best, most creditworthy tenants are getting the better deal or lower move in costs (savvy shoppers) and know the opportunity costs of money.