We are looking into getting a fixer upper and plan to rent out our original residence ( Zillow says we can get $2700 median rent in our area ) while moving and fixing up the new house.

Depending on the lender (bank or alt. lender) you have to look at origination fees....points, doc prep, interest rate, frequency draws are allowed/min. draw amount allowed per request, interest payments vs. interest reserve & whether interest reserve is capitalized to fully understand the true cash requirements.

I made a relatively low offer and after one negotiation we settled on a price that was about 45% lower than the original list price.

Understand Replacement cost versus original building costs. 

I was from CT and Boston originally.  

@Steve Powers is correct that these were mostly originated as owner occupied loans.

So you might as well be a head of the game do the cash out refinance buy the next 1-2 properties and simply refinance the original mortgage as a "rate and term" which carries a lower rate.

they make money servicing not originating new loans. 

I think some folks search for discounts so that's a way for being promoted.Seems guest dont rent a 4 bedroom house unless they have triple the amount of guests they originally reserved for.  

My markup is always lower than the original lender's because I don't spend money advertising during the Super Bowl, my president doesn't have a corporate jet, and we don't have layers of management we need to pay.