@Michael Dumler absolutely nailed it. 

So there are a few ways to look at this, the 1st question is are you sure your renovation’s will double the property value, most renovations on primary residences, your lucky to get 60-70% of the dollar cost back out upon sale, so really nail down your comps, than you have basically a math problem if your rate on your primary goes up how long if ever before that extra payment is more than 400k in taxes, that’s just a simple calculation to help you decide, but I suspect you actually have a different question here, from a purely financial perspective my guess is the best option is to do anything to avoid that tax hit, but one of the reasons to make money is to spend it on things that you enjoy, based on your overall financial picture and a subjective view of how much enjoyment you will get out of a renovated home, you should decide if you want to roll your profit into another deal or “cash-out” your winnings, I love cars and I’m willing to spend more than is fiscally smart on them because they bring me joy, there is nothing wrong with that, but i don’t think it’s a fiscally smart choice, without knowing your exact property id imagine a renovation would fall into that category, so that’s the terms I would use to decide.

That's where I think you nailed it. 

Jay hit the nail on the head with this one.

After reading the other comments, I feel like you hit the nail on the head!

Doesn't mean you can drive a nail straight, but means you're a decent fellow..... 

Hi, I've searched through a lot of credit unions and other banks and the cap on the HELOC amount I'm seeing is 250K.

There is no cap on how many DSCR you are able to have 

Other wise it will only do damage in my opinion.This is but MY personal preference and this doesn't mean what I say on this matter is factually correct.Other than that, you nailed it.

Unlike CA there is no Prop-13 cap on appraisals.