A number of reasons for not going down this route: A lot of those portable storage units/battery packs have limited power output. If you aim for the <$500 budget range, most only put out 200-300w. If you want up near 1kw, plan to spend over $1k. Also with infrequent use being in play here, all being lithium based I am wary of spending the money and having it sit and likely self-degrading as a result. Generators are also out for similar reasons. And more importantly they are just noisy and in the end likely run a lot less efficient than using the C-Max as a generator itself.
All in all going down this route I'm probably looking at $200-$250 all in for the inverter and all the extra bits and this will get me an 800w-1kw continuous power feed that the car should be able to handle just fine. And I can safely and quickly disconnect it and pack away the inverter when not in use and hook it back up just as easily when needed. This definitely isn't an unusual setup especially in the hybrid/plug-in communities. This is just the first time a personal need for this has come up and finding a very good setup to base off of.