You should get a credit for your premium dating back to the, date of loss. Or at least they should, we did on ours.
Our insurance was the same way, no extra $ for anything extra. We kept the tv, propane tanks, one of the propane quick conects, spare tire and holder, and i swapped all the tires, with old, wore out tires on my car hauler.
And i was able to negotiate the price up about $1,500 or so from original offer. We ended up getting the same amount for it after deductible as what we paid for it new with the hitch. Basically got the hitch for 10 months of interest!
When wrecker driver came to pick it up, (yes a roll back wrecker with a hitch attachment on the wheel lift) he told my wife that he was surprised that we had left the battery. He said most dont have them and its a real pain hitching when they dont. He also said he had picked some up without any wheels at all.
Just an fyi on time frame, ours was hit in a storm on may 20th, 2013, was negotiated and then picked up on july 24th and it took another month or so to collect all the checks and finish all the paper work. That why we waited till last Feb to order one, just didnt want it sitting there all winter.
Good luck with it all!