Forget throwing the money at an offshore genny and replace that little alternator with a high-output. WAY more bang for your buck. Your revised budget allows for you to have it installed and then some: probably still enough for that genny if your heart's really set on it....
Get yourself a decent AC charger for when you're on shorepower and you'll be set.
Just my .02
"Verbosity leads to unclear inarticulate things"