Wanting to take my motorcycle ... travel trailer ...

I would definitely not try to load it in the bed. In that respect a heavier payload truck isn’t going to help much. 850 lbs is way too much to easily deal with it in the bed and quite a steep angle.

I’m not getting why some think the tongue weight will go up too much considering most of the weight will be on or behind the rear axle.

I think you are on the right track with a toy hauler. Consider buying a used one and update it to match the comfort you want.