Firstly, congratulations on being in a position to pay down extra on your principal on a regular basis. It's a great way to knock that mortgage loan out of the way.
I'm going address this as a purely re-fi question first:
I presume that with your LPMI loan, you opted for a higher interest rate in order to bundle in the mortgage insurance in.
Currently (12/21/2018), Freddie Mac reports the 30-yr mortgage rate is 4.62%: http://www.freddiemac.com/pmms/
It generally costs between 2-6% to re-fi a mortgage loan, so the rule of thumb is that if you can lower the rate by 1%, it might be worth it financially: https://www.investopedia.com/mortgage/refinance/when-and-when-not-to-refinance-mortgage/
Given only these points of information:
- assumption that LPMI loan has higher interest rate than conventional loan at your
- current loan interest rate
- current mortgage rates
It doesn't sound like it would be worth your trouble to re-fi out of the LPMI loan, especially if you're not going to stay in the home long term.
From a tax perspective, you'll be able to deduct the interest from your taxes provided that you are itemizing. With the newer higher standard deductions of $12K single/$24K married (https://www.irs.gov/pub/irs-pdf/p5307.pdf, pg 7), it might not matter.
Outside of getting rid of LPMI and taxes, there's a third topic to consider: monthly cashflow vs emergency fund. If you re-fi (using partial or all stock options), you might end up with a lower monthly payment, which may ease things throughout the year. This will depend totally on the new principal amount (it will be lower) vs what rate you get. A new loan at $132K @ 4.62% looks to be about $745/mo (if you have an escrow account for $800 property taxes, value I used to mimic your current payment). This lower monthly payment will come at the cost of any potential emergency funds that you may have (or want to build up).
If I made a bad assumption, let me know and I'll re-visit this.
Hope that helps.