I would *definitely* go with weight distribution. Without it, my 650lb tonque weight brought the rear down (I think 2") - you can measure but it also caused my front to pop-up 1". It puts all the tongue weight directly on the rear and the front popus up leading to less sure steering. I don't believe it's the 'sway bars' that helped me so much as the weight distribution aspect!. Do both.
Weight distribution will push that weight forward and help keep the rear up higher and front down lower on the road - makes HUGE difference.
There are several WDH (weight distribution hitch) youtubes / explanations that might help you. I didn't go 'the cheapest' but lower on the recommended scale with a Blue Ox Trac Pro -
https://www.blueox.com/trackpro-weight-distributing-hitch/ because this type let's me backup as well. (Some of the cheaper ones dont' support backing up)
This Blue Ox Trac Pro absolutely stabilized my towing of 5300lb trailer and they make even better ones if you're willing to spend more $
And to reiterate - the vehicle is not the issue in my opinion. A truck wouldn't do any better.
