I’ve heard on podcasts that developing a depository relationship with small local banks could result in more favorable interest rates and more flexible loan products after some time with the bank. 

If you don't plan to occupy the home, I would love to a lending broker in the area to find you the best deal to either do an investment loan or DSCR type loan.

Any advice on if we should use it to pay off our loans against two of our retirement accounts (that we took out for the downpayment on the first STR) in order to lower the monthly bills or if we can/should cash out one or two of our retirement accounts (457 and/or 403b) and pay off the loans? 

The loan insurance company seems legit.

On the other hand, this lender is also very picky, for example they require 100% liquidity of the borrower, meaning someone would need $3m liquid to get this $3m refi (& you don't get to count loan proceeds towards that liquidity).

You may finance this using a DSCR loan if this is your investment property.

. $100k performing I/O note for $90k), how do you classify the extra principal you get back when the loan matures?

I leave one in the living area , rest replace with light fixtures, Renters never clan them and when i do get the house have to replace them . finally said heck with it. 

You're going to need to put 25% cash down since you'll be needing a commercial loan.

I'm looking to use the VA home loan.