Hrmmm...that gives me an idea.
How about a solar charge controller between the generator's so-called "12v" outlet and the battery? A 10a Morningstar PWM would probably work just fine.
For that matter, an MPPT unit might just load the gen's 12v outlet to some optimal power point and hold it there until the battery is done charging.
(And yes, a decent mains charger would work just as well and probably be cheaper. But what the hey, it's something to think about anyway.)
Current: 76 E-250, bubble-top, self-contained|couple of old Yamaha enduros
Previous wheelers: 41 Willys|78 FJ40|78 Bronco|84 Bronco|74 Ramcharger|78 Ramcharger|79 D150 PowerWagon|77 D100|79 D400 dually, converted to 4WD, utility bed, 10' Lance|75 Westy|69 Scout, RHD|bunch of others|bunch of bikes|couple of boats|couple of motorhomes|blah blah|so what|not my idea|just doin' what I'm told|wank wank|this space for rent|candy is dandy|but liquor is quicker