I must agree with others that your symptoms are most commonly associated with battery issues more than the starter. As Steve notes, you may best spend starter rebuild cash on the batteries instead. Check that the battery post connectors are clean of resistance-causing corrosion, especially in your case the two chassis batteries. Your having them load tested may provide insight. Also check the starter terminals for looseness or corrosion, and the chassis ground bolt.
But running the genset in the evening should’ve handled your devices plus still charged the house set. If they were that weak by morning, either corrosion is interfering with them also or they are at the end of their life and just can’t handle even simple overnight discharges. Or something in the coach is drawing more than it should overnight. Are there markings on the batteries or missing date “chad’s” on a top label that can reveal their age, and which may make simple age deterioration more obvious?
I’ve gotten 12 years out of my original batteries, much as Dad taught me back in the day with farm equipment batteries. But I try never to overdraw them, even the deep cycle house ones. Frequent deep discharge does the quickest harm, and many owners are lucky to get 5 years out of them. Practice keeping their state of charge (SOC) above 12.5 volts; at 12 volts they are 50% discharged, and you don’t want that if at all preventable.
Also keep in mind that when on park power or genset, the house set gets charged first. Then upon reaching about 13.4 volts float, your BIRD kicks the Big Boy solenoid over to recharge the chassis pair. The reverse is true with the engine running where the alternator does the chassis set first and then at 13.4v gets kicked over to the house ones. Some people overtax and burn out their alternators, dry camping that way, by not boosting the house set with the generator first before breaking camp. Alternators for these coaches, as many here can attest are spendy. But unabused they can last the life of the coach.
Joel