$10,000 to invest in the house - Pay down principal or spruce up to increase appraisal?

Hypothetical but not totally unrealistic situation:

Looking at recent comparables (and non-comps like smaller homes or fewer amenities), the value of homes in my neighborhood have increased dramatically. My 1.5-story 1675 sqft 4-2 home used to be the most expensive on the block at around $136k and everything else was listing in the $90s; now, with the economy picking up but money still cheap, other houses in my neighborhood are changing hands at contract prices approaching a quarter-million.

Now, we bought in 2010, and didn’t have enough for a conventional mortgage so we went FHA and are paying a PMI on our current note. I expect, in the next couple of years, to be able to spend $10,000 on my home. The question is, how best to use the money?

• Option A: We could use the money to pay down our mortgage directly. $10,000 off our principal wouldn’t quite get us to 20% and allow us to lose the PMI, but it would drop the P&I chunk about $50/mo and get us within a few thousand of 20% based on the sale price; we could then make a couple extra payments from there and lose the PMI based solely on equity of sale price.

• Option B: We could use the money to fix and/or upgrade some things in the home that were part of the original bill of sale (like a hot tub in the back yard that raised the list price way more than it should have given its condition), along with further improvements or repairs such as updating the kitchen and bathroom. Then, we hire an appraiser, he prices the home, and any increase in the value over the purchase price is pure equity for us; if the appraisal reflects neighborhood price increases, we could end up with better than 50% equity.

  However, there is a chance that the appraisal could come in at something less than a figure that would give us 20% equity. It’s not a likely scenario IMO given what the neighborhood’s doing, but not impossible. Then we’ve spent $10,000 and still have the same housing payment, plus the appraisal will be reported to the tax appraisal district and be used to calculate our tax bill, so we could pay the money and see our housing bill increase further.

Of the two, Option B seems more palatable; the assessor is going to look at the surrounding homes’ sale prices anyway, and adjust our home’s assessed value upward by as much as he can (State law restricts tax base increases to 10% over the previous year’s assessment, which for my house is still below the sale price) for 2016. So, we might as well get a number for the home’s true value that will let us drop the PMI even if it’ll be offset by increased property taxes. In addition, our credit’s improved since we bought the house, so in the re-fi or streamlining to drop the PMI we could also negotiate a lower rate.