I'm not a full-timer, but I feel your storage issues. IMO, that is the biggest draw-back to truck campers. I have a storage box on the roof that I use for relatively light items that I don't need often, or come out and stay out while I am at a campground.
If you put something on the front, make sure there is a clear path to your radiator! I made that mistake last winter. After you set your gear up, walk a couple of feet away and look at your truck. If you can't see at least 75% of your grill, then don't do it. You will have overheating problems.
I have a rear access camper too, I know what a pain it is to use a carrier on the back. If I'm not hauling a trailer, I put my carrier on the rear hitch and that's where I carry my generator & fuel. It is a pain because if we need to get into the camper on the road, I have to unstrap the generator and roll it to one side.
I've seen a lot of people with small enclosed cargo trailers like the kind you can get at Lowes. Don't know what your budget is, but that might be an option to look into.
Here are some examples, the prices tend to go up from there:
Example 1Example 2