Need some guidance

[Ricky]

So I have a 08 Prostar with a ISX and Ultrashift. I replaced the factory 1200 watt inverter with a Xantrex Freedom SW 3012 3000 watt inverter. I got it for 230.00 from a guy that upgraded his RV. It works great and has the control panel also. I did the upgrade because I use the inverter to run my roof mount AC. It's a Coleman rough neck 15000 btu and I installed a easy start. I only use it while driving and on high it pulls 1500 watts. When parked I have a generator that I use to run it. I do mostly short haul and I usually have my two French Mastiffs with me. That's why I like the roof mount, I have problems with the bunk AC. I used the setup last year with my 1200 watt inverter and just did the upgrade. It has been really muggy this year and the 1200 watt was kicking off. It used to only pull about 1150 watts but that was on low. But my issue is the new inverter is pulling the battery voltage (by the control panel) down to 10.9 at 1500 watts. Batteries are 1 1/2 old 950/1100 and are a good battery. Alternator is a 215 amp and is about the same age as the Batteries. So to keep from messing something up in the long run, what should I do. Bigger Alternator, deep cell batteries, both??? I talked with a place here about building a bigger Alternator from the old one I took off before. They said that they would have to look at it before they can tell how much they can bump it up (the numbers are not on it). What are the pros and cons doing that or buying bigger. My front AC works pretty good but the rear is a pain in the rear.