I find his "disappearance" and evasion of our property manager for the last 2 weeks inexcusable.However, I am considering making the tenant an offer to evict him "lightly", i.e., he pays for this months rent, pays my attorney fees, and gets out within a week.

Tax evasion is a choice.

How would an auditor be able to tell the difference between a $300 withdrawal to pay a contractor and a $300 cash withdrawal to put in your pocket (i.e. tax evasion)?

Quickbooks is for "bookkeeping" - a good CPA will help you with tax avoidance [not evasion].When you form your LLC, be sure to use a competent REI attorney to setup it up for you and DO NOT do it yourself.  

I live here in Homestead Fl a 3/2 1900 Sq ft.I began renting this home on 7/01/2015. with a standard written yearly lease. I was never told the house had been in foreclosure since 11/01/2014. In fact on day of origina...

The contractor doesn't want to fill out a 1099 because he wants to do this "under the table" Technically speaking, that is tax evasion, so there's that downside.

Sorry to be evasive, but it all depends on what your objectives are. 

Where is your HUD-1, 1099's, required disclosures, where is the audit trail of escrow deposits and accounting of you paying off someone's mortgage, ever hear of federal settlement requirements or ALTA, money laundering, tax evasion, ?

(tax evasion, liquor violations in bar business, slumlording, etc.).

If they are evasive then you likely have a problem tenant on your hands Did you screen them properly?