Just some thoughts from my experience. I'm having similar issues that you are I believe. My tongue weight is really low. Like 450 -480 pounds (sticker) on a ~5,000 lb camper. It feels too balanced to me. Almost like the axles should be back a couple feet in my case. I think they do it that way so they can be pulled with heavy suv's with low tongue weight. All my tanks are in the rear too. Anyway, I put a generator rack on the tongue and that helps, but I'm not always taking my generator either. Usually just to the race track where I have no power. That might be something to look into. If I'm not taking my genny, they I throw coolers or whatever else is somewhat heavy on it.
I have airbags, but with such little tongue weight, I have found them to be of little help. I think my ride got worse with more air. I use them mainly just for heavy bed loads now. Otherwise they are just set at the minimum 5 psi or whatever.
I'm really hoping heavier tires will help fix both our scenarios. Getting e rated tires switched over on Friday. Sadly, were done for the season so I might not have much time to try them out. I'm going to hook it up one last time on the way to put it away, hopefully this weekend, and report back.
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