Refinance, extra principal, or both?

I plan to stay in my house for 10 more years (at least). I am currently about 2.5 years into a 30 year, fixed rate, $ 200K mortgage at 6.625%. I have been paying $ 300 extra principal a month, so my current principal balance is about 190K.

I am considering refinancing to 30 years @ 5.125. I’d pay a point and closing costs around $ 4500 (unfortunately, I’m in Massachusetts), which I could also finance for a loan amount of about 194.5K (or I could just pay closing costs in cash).

How do I figure out if I should keep my current mortgage and keep paying $ 300 monthly (or more) extra principal, just refinance, or refinance and pay in extra principal (I could afford to pay in even more than $ 300 with the new lower payment)?

Also is there any advantage to paying the closing costs in cash vs. financing them in to a new mortgage?

This is confusing. Also any opinions on which direction mortgage rates might go over next few months? (I know. Stupid question lol.)

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