In fact, I'm just remembering now that I was one of those buyers who didn't have sufficient 1st-mortgage lending for the whole deal. 

With that said, you technically can refinance any time you want after you close because these conforming loans generally have no prepayment penalty.The other aside that I will mention is that you will want to make sure you have sufficient comparable sales in your area that will be able to document enough value before you spend money on a non refundable appraisal.

The worst part about holdovers is the waiting period if you fail to provide a timely, or sufficient notice.

The denial was based on lack of sufficient cash flow and credit, not from clearing out a case of beer!

Different opinion, if you are already cashflowing sufficiently at current rent, I wouldn't up the rent to market right away. 

You probably wouldn't have sufficient cash reserves to deal with a potential maintenance emergency.

If this was a brand new house then your number would likely be sufficient.

It sounds like you probably didn't do sufficient due diligence on this guy and/or don't know him well enough to predict how ethical and trustworthy he is.

If they don't know how to arrive at sufficiently good answers - THERE'S their answer! 

Without a deposit you fail to meet sufficient consideration for a bilateral contract.