It does sound like the alternator is gone, but there is a small chance that the battery isolator is gone instead of the alternator. With the engine running, check the alternator output terminal with a meter and see if you are getting 14V or so. If so, check the battery banks and see if either are seeing the 13.5v or so. The isolator is between the alternator and battery, if they are not.
If you have a continuous duty emergency boost solenoid, I think it is a very good modification to change the momentary rocker switch to an on off type. I did that on my last coach. When the starting battery is that low, you can put it in the on position and leave it. You would start the generator and the inverter/charger now has the ability to charge the chassis batteries at a high rate. The echo charger will not recover a dual set of dead batteries, and using the alternator to do it is a tough job for it. The only down side is forgetting and leaving the switch on. That one is solvable, and you get to not buy new alternators...
Later Ed