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I would want to use something like my 922cc V-twin 30hp 26kw surge 17.5kw running. That way it could provide most of the needed drive power and level 2 charging while going down the road.
I have compared inverter generators to fixed speed and found the inverters have almost no fuel savings above half load compared to direct drive counter parts with the same rating. Nearing full load inverters some times do worse on fuel. Inverter generators beat direct drive at low use.
Also that 5kw generator is likely only going to be able to make around 4kw continously.
I have heavily modified my generators to get near full output continuously. Consumer and contractor generators are only designed to run at around 80% continously. All can hold a 100 to 110% load but will burn up in short order.
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1984 chevy suburban, custom made 6.5L diesel turbocharged with a Garrett T76 and Holset HE351VE, 22:1 compression 13psi of intercooled boost.
1989 firebird mostly stock. Aside from the 6-speed manual trans, corvette gen 5 front brakes, 1LE drive shaft, 4th Gen disc brake fbody rear end.
2011 leaf SL, white, portable 240v CHAdeMO, trailer hitch, new batt as of 2014.
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