What your experiencing is similar to those with toy haulers which are the TT type(not 5ers). The weight behind the axles has a serious effect on tongue weight and handing. As another post mentioned, if your fresh water tank is in front of the axles, try filling that. This could be the easiest fix. Other wise a premium hitch setup may be the only fix.
Is your trailer level or slightly nose low? If it is nose high or even level, try lowering the hitch 1 hole. Might be the ticket.
I feel that some of the manufacturers have not done a very good job of designing the longer TT's. Floorplan seems to be the only priority without actually thinking about the trailer functioning correctly after it is loaded.