I obsessed over this topic for about a year.
What I found is that the best and most realistic bet is to look at credit unions. They don't advertise. But many of them offer "promo rates" from time to time.
e.g. I am in the process of refinancing with Sikorsky CU advantage morgtage for 12Y term @2.5% and $749 total closing cost.
https://www.sikorskycu.org/Borrow/Loans/Mortgages/Advantage-MortgageI don't know if they lend outside CT (probably no, they seem hyper-local to CT based on my interaction with them so far), but maybe worth a try to call them if you want.
Someone in this forum had previously suggested some similar product from rbfcu (
https://www.rbfcu.org/home-loans-realty/mortgage-refinancing) to me. rbfcu told me they won't lend outside TX (not sure if that is a permanent thing or they are just swamped and hence don't want to deal with out-of-staters). But you are in TX, so perhaps give them a call!
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As to which term - 30Y vs. 15Y vs 12Y or anything else - I was primarily looking at the APY/APR. I have tried to convince myself to treat the home equity in the most mathematically optimal way (i.e. take out as much money as possible and let it ride on fixed rate non-callable leverage - the best kind of leverage that is out there). However, I figured out that I hate borrowing in my guts. So I decided not to overdo it. I'm just doing a refi to a 12Y term and will let that ride down to 0 in 12 years.
It's likely best not starting from mathematics when dealing with this question, but rather as a "what makes you sleep better at night" question. Once you have figured out what makes you more comfortable, you can always invent some rationalization. e.g. my favorite one is "principal payment is a bond-substitute and hence better for asset allocation in conjunction to my stock heavy portfolio" - never you mind that I never include my home equity in my net-worth calculation.
The opportunity cost of either using or not using this leverage (even a fantastic one like the US Government subsidized, non-callable one like a mortgage) is likely not going to make or break your portfolio in the long term - so no use fretting over it. Just do what makes you sleep better! IMO.