I would insist on the Equalizer of a weight rating recommended by Equalizer as that's what you and the dealer agreed too. Too bad (I assume) it's not in writing. Use the safety argument with them and it is a legitimate and valid argument.
We tow our 32.5' TT without any sway control and no sway. Are you sure it's sway or just gusts and passing trucks pushing you around a little. For us, sway control was me telling my DW she can load all she wants into the trailer as long as it's in front of the axles. Get the proper hitch, keep the tongue heavy and enjoy your new TT.