Separate out the property taxes question from the refinancing question. You can have your property taxes reviewed any time.
The rule of thumb for refi is if you can get 2% or more reduction in your current interest rate, AND you are going to stay in your house for 5 or more years, do it. (This is presuming you want to eventually pay the mortgage off--some people don't care.) There are costs involved, and you want to stay in the house long enough to make up the difference in cash outlay.
As for the two companies you're dealing with--they do have to give you a good faith estimate of all closing costs, and your interest and payment, etc., but I've never seen one that was even close to the actual numbers until five minutes before the closing! Since you're doing the special program, I would think they should be able to pin it down a little better ahead of time. If you don't mind financing a couple grand in closing costs for 30 years, go ahead and allow them to roll them into the loan. Since my goal is to pay as little interest as possible, I'd rather pay it up front.
Anyone who said they are making decisions for you, getting a little cash out, whatever, I would run away from screaming. I'd say go with the bank, not the mortgage broker.
Karen
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insidious ungovernable cardboard