All very good reasons why something like a pusher trailer of some sort would be ideal for you. Sure it might have a relatively high initial cost but I don't think you'd have insurance to contend with and I'm also not sure about tab fees in your state. In my state I believe anything that touches the road(so not something like a receiver basket) needs to have tabs. True it would probably be pretty cheap($20 ish) and with some trailers your able to purchase lifetime tabs for not much more. The other option of a receiver basket and 30a 240v generator to charge when not driving, this is again somewhat costly(~$1000??) and I personally wouldn't feel too comfortable carrying around a 250-300lb generator a foot or more behind my Leaf.
I know you kind of nixed a PHEV and I don't believe there is currently a good choice of one that is spacious and has as long of a EV range as a Leaf. The newer Volt would somewhat work but it's range is 20-30 miles less EV than a 24kwh Leaf and is quite cramped IMO, all around. The older used Volts are somewhat reasonably priced($12k range in my market) but they even had less EV range(40 miles I believe) and they were also only 4 passenger. Another disadvantage of a PHEV like the Volt is I believe keeping it on EV only gets to be rather tricky in the winter, it keeps wanting to start the ICE for heat! If your willing to put up with maintaining a second ICE vehicle, a single PHEV wouldn't give you any more maintenance such as oil changes and would save on insurance/tabs, etc but again in the cold could be an issue.
Another option but even less of a EV range than the Volt and definitely more costly would be a PHEV Chrysler Pacifica. 30 mile EV only range, decent ICE MPG, room to haul 4x8 sheet goods or 7 passengers. The downside other than the 30 mile EV range would be ~$40K cost, including the $7500 federal rebate due to it's >16kwh battery. I was/am seriously considering this option although I'm not sure I'd want to drive around/park something as large as a full sized minivan for my daily driving. I'd also kind of like a 60 mile EV range but I guess you can't always get what you want.....
AFA a decent full amperage EVSE, in your case I'd strongly suggest something like my ZenEVSE which is very portable(about the same size and weight as a OEM Leaf EVSE) works on both 120 and 240v and is adjustable to 4 amperage settings that you chose when built. You'll have to be kind of handy, making various outlet adapters such as I did, they end up costing ~$20-30 in parts. You may be able to purchase them too, I'd guess they might end up costing $30-60, if you can find what you want. My Zen EVSE ended up costing a shade <$300 including shipping from China.
I chose mine to be fitted with a L6-30p(plug) because IMO thats the easiest, cheapest and most compact end to adapt to various other plugs although you could also go with the most common 14-50p which Tesla has kind of standardized and your most often to see in a RV campground.