Off topic, but fwiw I bought an Ego push mower last year (from my local Lowes). I have been pretty happy with it. Handles my 0.42 acres just fine. Even if it didn't, it recharges so fast that I don't think it would be a problem. In concept if I had a really large yard I could just get the mower + one backup battery and mow forever, because the battery charges faster than I use it, so I could just swap them over and over. For now though the one battery is fine.
My plan is to get a mower and string trimmer, both with batteries (though they will be different amp-hours) and then expand my tools as needed - pole saw, chain saw, etc. Ego even has a pretty beefy looking electric snow blower, which I think I could get behind.
I'm just a little extra cautious because I like to mulch my leaves instead of raking them, but sometimes I rake them into a giant pile and drop my mower on them. My 160cc lawn mower handles that just fine, and if an electric can put out
more torque than that, it wold be great.
I know it can recharge from the bed or the frunk, but I'm not sure if that capability is shut off while driving. I wouldn't think it would need to be, as if it needed to momentarily draw a lot of power for climbing a hill with your foot down it could easily cut power at the outlets.
In your situation I'd definitely have an electric lawn mower. I've already gotten rid of everything else that's gas powered, as I don't need a "real" chainsaw and my yard is small enough that the 16" corded one will suffice for everything I need it for, save felling a tree, in which case I'd borrow/rent one like I did several years ago.
My Ridgeline has a 150W/400W inverter plug in the bed. It will be powered while driving, but only at 150W. I
think the 400W only works when idling in park. The feature is still useful, but not ideal. It would seem with the F-150, if it could power your house (extended battery), then it
should be able to recharge some batteries while driving.
I've had the same gas lawn mower and string trimmer since I l moved into my house in early 2008. The gas mower has been great (still starts on its first pull,
maybe second) with nothing put yearly oil changes and spark plug and filter changes every ~5 years. The 4 cycle trimmer has been a bit more of a pain, but it's fine. My thing is, even though my yearly maintenance isn't that much, why even go through that? An electric, provided it meets my needs, would be better in all respects. It just costs money. (The mower and trimmer I'm looking at aren't cheap)
I kind of feel the same way about electric appliance cars. Why go through maintenance on an appliance if you don't have to?