I have a choice to make on which lender to go with on my rental property refinance, however as I research each lender, I cannot find adequate information about their actual business practices.

What's the best way to beat an all cash offer as is with no contingencies and a quick closing?  

---You could offer to let them out of the lease---Refund the cost of the test---Spend up to $x to address the issueYou should explore the consequences/expectations before agreeing to anything else.Second, allow them to get a test done by an inspector you approve. 

@Joseph CrawfordThe FHA and VA loans offer a lucrative field in real estate investing.

Find Brandon's videos on YouTube for the "four square" method of analyzing homes and practice.

The custom builders in the area are very competitive and are offering pretty inexpensive builds vs comps.If the lot was purchased recently for 20K and the turn-key cost to build is $200K, after I close on the house (bank said appraised value would be 220K), would a new buyer have problems with it getting appraised over $220K even with other comps selling for 300K+?

We offer renewals unless there is a serious issue anyway.

Under this method you make your one and only offer; no negotiation, if it’s not accepted you walk away.When I started in real estate investing a couple of hundred years ago, I was a proponent of the first method.  

If you could offer me the same generosity, it would be wonderful!

Have couple of offers to buy, one is convenience store and the other is storage company.