Internet suspension diagnosis is always to be taken with scrutiny. With that understood here is my input.
You have a newer model 2551 on an E450 chassis, meaning that your chassis is about the least loaded as an E450 could be.
Heavy duty front and rear stabilizer bars would reduce side-to-side rocking motion. But if your rig is not doing that while you compensate, your compensation troubles might get resolved with a rear trac bar. The trac bar reduces horizontal side-to-side motion referred to as tail-wagging. Either type of such motion can require steering compensation as you describe. Determine what type of behavior your rig has, rocking or tail-wagging. Then consider the appropriate resolution.
You are correct to address the play in your tow bar through one of these (called a Quiet Hitch) and see if it helps.
Be sure your tow bar is horizontal. If not, buy something like this to make it so, and get the right height as they are sold in different off-sets. A tow bar on an angle greater than a 2" height difference between motor home and tow vehicle can create notable bucking. The greater the difference, the greater the bucking action.
Though it is not the problem you describe, it is worth mentioning since you brought up the play in your tow bar. Adding a riser will introduce a lot more play in the tow bar, so be sure to use two Quiet Hitch U-Bolts there.