Another vote for the Hitch Vise and I've been using it on my 7500lb trailer since around 2008 and wouldn't leave home without it. Not only does it COMPLELETY ELIMINATE any movement, but IMO it prevents the long term wallowing out of the hitch pin holes in the receiver over time since it dampens/softens up the push/pull - wobble of the drawbar in the receiver tube. This is something that takes years to happen, but I have had it happen after about 10 or 15 years of towing fairly heavy TTs.
IIRC the directions say it's limited to trailers under 5K, but even with my heavier trailer I have seen ZERO downsides to it's use. I did upgrade the bolts to grade 8 for better "clamping" force and use a torque wrench for tightening to get proper and even torque on the bolts.
Larry