I understand that most banks like to use this formula: (Value of home - amount owed) .8I have enough equity in the home to where 80% of the difference in value minus balance is sufficient to fund my construction project. 

To my understanding the banks don’t usually show the house and you’d have to buy it “as is” but how do you know when you have a gem on your hands or fools gold?

If you were going to be making a purchase in the next 3 years would you keep your money safely "under the mattress" in the bank, or would you place it in the market and accept the risk for the possibly great rewards?

Because its (supposedly) from a foreign bank, it may take your bank a while to figure this out. 

In this order:Franklin SynergyReliant BankCedarstone Bank (Probably will only do a 15yr term)Civic bank and trustFirst Farmers

Spring Valley Bank is very investor friendly.

On a similar note, a few years ago the foreclosure sale at the courthouse used to have 90%+ of the properties go to the bank, and the bank takes a hit on the price and offers it as an REO. 

If the bank finances 80%, the seller 15%, and you 5% and the numbers still work with a higher mortgage, you can buy for very little money. 

I was able to get an in contact with a small bank and they told me 6 months after I'm in title ( I assume it would not have to be fully rehabbed in that 6 months) and if I live in the property it would be 80% , if I don't it will be 70%.

Typically big banks and credit unions are captive to a single PMI provider, mortgage brokerages and banks can shop it among mortgage insurance providers.