Without actually building the 3rd unit, would this new triplex eligibility increase my property's value? 

Only reason I've been doing it is to get 0% business credit card limit increases.  

It's tempting early on to leverage as much as you can so you can do more deals and keep liquidity, but increased cashflow especially with PMI will make you sleep a lot better at night.

The shorter the prepayment term has an impact on increasing the rate.4.

It’s just going to slowing increase with inflation.  

The shorter the prepayment term has an impact on increasing the rate.4.

I'd underwrite the property, with that low interest rate assumable mortgage, to cash flow positively from day 1 as a long-term rental, but be willing and able to use the rent by the room strategy or to rent out part of the property as a Short Term Rental to dramatically increase cash flow during my occupancy. 

That then registers the property at a new “base rate” and your future rent increases all be “base rate” + Inflation as guided by the town.

Again, your time and energy is better spent increasing accountability and pushing RAD to improve their staffing with individuals qualified to maximize their portfolio at this time.....and in the future spend some time and money to perform adequate diligence before you invest passively. 

Additionally, the house is 25 years old and could use cosmetic updates to increase rental appeal.