[disclaimer: I am a heat pump technology developer, however the following is just low-effort notes and mental calcs of low reliability, they may be of interest to some. YMMV]
It may be better to invest in improved insulation.
As rough rule of thumb COP is = eff * Theat/(Theat-Tcold), with Temperatures measured in absolute degrees (Kelvin or Rankine), eff for most domestic heat pumps is in range 0.35 to 0.45, high quality european units are often best for COP due to long history of higher power costs—but they are very expensive, frequently $10-20k
Looking at the COP for the unit you quoted the eff is only about 0.25 at rated conditions, not good, unless you get a much larger unit and run it at a less powerful more efficient load point.
That’s a pretty huge electricity price, about 4.5x gas price (which is distorted-market nuts, 3x is more usual globally). Given that differential it might be better to look at an absorption heat pump like https://www.robur.com/products/k18-simplygas-heat-pump that gives up to 1.7x gas heat—though they look to be on the order of $10k.
Here’s an annoying fact; If you ran that $2/therm gas (~$0.07/kWh) through a reasonably efficient (~40%) natural gas genset it would produce electricity cheaper than what you currently pay for power, and you would have 2/3rds of the gas energy left over as heat. A genset in your neighbourhood could provide a few 10′s of houses with cheaper electricity and low cost waste heat, though no doubt prevented by regulatory issues. There are a few small combined heat and power (CHP) domestic units on the market, but they tend to be very expensive, more tech-curios than economically sensible.
I’m going through this too with my kids. I don’t think there is anything I can do educationally to better ensure they thrive as adults other than making sure I teach them practical/physical build and repair skills (likely to be the area where humans with a combination of brains and dexterity retain useful value longer than any other).
Outside of that the other thing I can do is try to ensure that they have social status and financial/asset nest egg from me, because there is a good chance that the egalitarian ability to lift oneself through effort is going to largely evaporate as human labour becomes less and less valuable, and I can’t help but wonder how we are going to decide who gets the nice beach-house. If humans are still in control of an increasingly non-egalitarian world then society will almost certainly slide towards it’s corrupt old aristocratic/rentier ways and it becomes all about being part of the Nomenklature (communist elites).