HARP refi or hold off?
I am not a big fan of Green Tree, i have had issues dealing with them myself. I do not like to talk bad about companies, so i will leave it at that. I think the best thing for you would be to look around at what other options there are. The rate they are quoting is not extraordinary. the reason they are saying no...

Can I get a the best possible mortgage rate with a credit score of 737?
Most loan programs now are credit score driven. what that means is that the higher the score, the better you will be able to do as far and the pricing hits. Besides your score, there are a lot of other factors that lenders adjust the pricing. For example, type of loan, loan to value, loan purpose. With your...

If our rate is locked, is it possible to re-negotiate rate if it went down?
it depends on what the lenders policy is regarding float downs of the rate. some will do it, but at a cost to you. Even if they do lower the rate, it may not be as good as what is out there on the market now. I would look at how big of a difference in the rate between what you are getting and what is available now to see...