Repot them so the stem is down in the soil and only an inch or so is above ground and take care of them. As long as their two little round leaves are on there they should recover.
Gas, there is no such thing as electric. That would be an inverter that uses car batteries. You would need dozens of car batteries to run your equipment for maybe an hour...
It can run "up to 30 hours" on one tank of fuel. That doesn't mean that it's rated to continuously run for months at a time. You can get big industrial generators that are designed to run continuously, and this one you linked may even be fine. But that doesn't guarantee that it will be...
It's not a practical solution. No need to even consider this. Backup generators that people use for their homes or business are gas powered. Not to mention that they are not intended for continuous use.
Which one are you looking at? You mention $90. The cheapest is $109 and would barely do a 2x2. The QB2000 which is the one that pops up when we click your link is $179. That QB2000 is not good enough for a 4x4 by itself. You will need a bare minimum of 2 of them. 2 of the QB3000 would be...
2-3 months isn't enough time. A fast grow is about 4 months. I think you need to get your expectations changed.
They will smell, even when tiny. But it won't be bad. Once they get several weeks old it will get stronger, flowering is when it's really bad and the filter is necessary.
As...
Perlite and vermiculite are polar opposite and should never be used together. Perlite is used in soil to help drainage. Vermiculite is used for the exact opposite reason, to retain water.