Coleman popups tend to be heavier than other brands, mostly because the entire line uses closed-channel tube framing, while others use C-channel for anything but the heaviest popups. The Bayside has always been the porker, and like I said, you should not believe that 2600 is your empty weight. By the time you load it up, you are likely right at the GVWR (3250 IIRC), and likely more.
Standard TW recommendation is 10-15%. But because the Bayside (and Mesa) has that large front storage trunk, they design the layout to be tongue-light assuming you will actually load the trunk with stuff. Since many people only put light stuff in there, your sway problems are probably due to having less than 10% TW. A sway controller is good insurance against wind gusts, passing semi-trucks, and the emergency lane change. But it's no substitute for proper loading. You need to to have the camper weighed (axle weight and tongue weight) and be sure you have at least 10% of total weight on the ball (preferably more). Once the weight distribution is good, the sway should be largely gone. Then the friction sway controller will be peace of mind for the unexpected.
Your Bayside has electric brakes. Do you have an electric brake controller in the Explorer? If not, you are severely overworking the truck's brakes. I highly recommend the Tekonsha Prodigy, P2, or P3 brake controllers. Original Prodigy may not be available anymore (replaced by the similar P2, which is currently the best bang-for-the-buck). P3 is functionally the same as P2, but has a more expensive, user-friendlier LCD display/interface.