The OEM towing harness is definitely NOT the place to wire your camper into - it is probably 12 AWG at best, and is much longer than needs to be. You should definitely replace this with some dedicated heavier wire. However even this won't totally fix your issue - the alternator output on Tacoma's tends to be on the low side, and at least on the 3rd generation Tacoma's it is an ECU controlled alternator and throttles back once the starting battery is charged. You could consider a DC-DC charger, which would allow you to get a decent charge from your alternator while driving. I don't have one of these, but others with experience will likely chime in, and this would really help with option 1.
Option 2 is always a possibility - with the bonus of coming with a shower!
Personal opinion, but option 3 would be WAY down on my list. I can't think of much more miserable than sitting out in the wilderness listening to my generator (well it would be even more miserable to listen to your neighbors generator). With a combination of fixed and portable solar (and occasional driving) you should be OK. Many folks (myself included) run this way indefinitely with no issues.
Finally, I wouldn't put much stock in 'HandyBob', not only is he rather bloviated, his recommendations are majorly out of date.