I tow with an Equalizer as well and never have sway issues even though a smaller trailer at about 28 feet.
Just another thought other than the usual already mentioned is it may be worthwhile to take a trip to the scales and way your trailer. Many times on the forum over the years people go to the weigh scales and the weight is not even close to what they thought and especially tongues weights as they can change a lot based on loads and options in your unit that may be different from the brochures and spec sheets.
You may find that your tongue weight is ot what you require and maybe the tail is wagging the dog due to that. It is a low cost method to confirm before doing anything drastic so may be worth a try.