Some cars have "generators" onboard
I have to say on a rental unit, none of your options are particularly pretty. But 3600W was the power output rating of the 2004-06 Silverado hybrid pickup truck, just to point out it's not a particularly demanding load for a hybrid or an EV, and 18 years later even the Ford F150 hybrid can do it :) as well as the Hyundai/Kia electric car platforms and several others, I'm sure. That platform looks really good, though their 12 minute DC fast charge isn't gonna happen on a Tesla charger because of Tesla's 500V limit.
The 3600W number is popular because that is the power rating of the TT30 socket used on small travel trailers that are fit for towing behind a car. See how nicely that works? It's also the capacity of a European household socket.
A typical EV has a 50-100 kWH battery pack, so every 2-4 days you'll have to come down off the hill and hit a DC fast charger. A hybrid will start its gas engine periodically to recharge the hybrid battery pack.
A lot of "Menlo Park" is up in the hills near or above I-280, so I presume if you're having outages for days, you're up there.
You need 240V, probably
One gotcha with a heat pump is it's probably a 240V load. That will limit your choice somewhat, because some cars provide 120V/240V (with neutral) and others provide only 120V or 240V without neutral. However, this problem could be solved by adding a 5 kVA transformer To the generator circuit to synthesize 120/240V from whatever the car can give you.
A "portable power station" won't cut it
And the reason is your energy appetite. You wouldn't be telling us your normal usage if you had any intention of scrimping on energy use during the outage, and the heat pump is your 'killer app' you need for heat. So a fairly costly PPS aka "solar generator" has 2 kWH of power, that'll run your house for 3-4 hours.
If you were able to retreat to a gas furnace, particularly an Empire or Williams style no-electricity-needed type, that would be a game changer.
For instance, a refrigerator has an appetite of about 1 kWH per day and that is viable with one of those PPS's.
You can crunch the numbers, 15 kWH/day usage means 60 kWH for 4 days and that's an EV battery right there.
Unless you want to own an EV, your best bet is a generator.