This is why wholesaling doesn't work and why the stock market is an awful gamble.

In every world this is a mathematically inferior situation to paying less for the property, unless you are willing to gamble that the 10-40k is a drop in the bucket because the place is going to explode upwards in value...?

Unpermitted may not be a huge deal in some cases, but when it comes to egress and life safety issues you're gambling more than I closed off the dining room and made an extra bedroom.

So unless you are willing to gamble with your savings, you do not save much time buying turnkey.

You are correct that market appreciation isn't a blind gamble, but it is speculative.

So essentially I am stuck either investing out of the state (20% down) OR gambling with rent increasing (possibly negative cash flow for a bit). 

Your stock market losses offset your stock market gains, your gambling losses offset your gambling wins, etc. 

This is the bank's gamble to try to meet their criteria, for example, Lets say the market conditions are stable, and marketing times are 30-90 days according to the agents BPO, or an appraisal, the bank might be inclined to accept offer #1 with a 30 day close and keep the other 2 offers as back ups.

Don't make the mistake of thinking you can reduce it to a bunch of formulas, some sort of gambling system.

So, it's all a gamble choosing one because of HQ2.