You likely need to be in a very hot market to have a sufficient buyer pool at this price point.You do not state the condition of the property. 

There is sufficient equity at the numbers you shared to do so.When the owner of record (with the tax lien) sells the property, the tax lien will be satisfied from the proceeds of the sale from escrow, prior to the seller receiving any of the sale proceeds.

This is all assuming I am able to find a property that cash flows sufficiently to where my living expenses would be paid for by the tenant I rent the second unit of the duplex out to.Sound insane?

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.