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Have you shopped around to see if you can do better than 4.75%? Perhaps on a 20 year loan if you can afford it, so you set your schedule ahead instead of behind, but even on a 30 year, you are only 44 months in, which is really early for the amortization. The portion of the principal paid only increases less than $200/month for your numbers between months 1 and month 44. Half the amount of your PMI. Pretty negligible overall.
I just recently did a refi and although I went with a 12 year loan (at 3.74%), one of my options was a 15 year at 3.99%. And mine is a junior/baby loan, which is usually at a premium and it was a $0 cost (truly, not rolled into the loan) refi.
The reason we got such a good rate was that our credit scores were over 800, as you've said yours are. We got a .25% reduction just for that, due to a state program, apparently. So ask around a bit more. We went with a credit union, rather than a bank, for this reason.
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