+1 for the solar and bed mat. When I bought my first Lance the dealer insisted there was a bed mat in the truck before I took delivery of the TC.
As far as solar, I never had AGM batteries installed, just standard deep cycle Interstates. I had lots of use and 9 years on my last Lance and the Onan genny had about 90 hours on it. It was run mostly for maintenance and occasionally for the AC or microwave. I almost never needed it for topping the batteries.
BTW you mention purchasing an eu2000i companion. Do wou already have an eu2000? My eu2000 runs my 13500 Dometic AC without the companion.
Make sure your charge controller can handle the AGM batteries. My current TT has a massive 4d AGM and the original owner disabled the stock charger and installed a separate charger made by SEC that is specifically designed to charge AGM's. Seems a reasonable precaution since this battery would cost over $600 to replace. There is also a solar panel with good Sunsei 20000 controller that charges the battery. Most of the time that's plenty and I don't need to connect the SEC charger.