Good call on the Dexter wet bolts. Their EZ-Flex equalizer is also a good idea. We have both. The OEM cheapo/cr@p plastic spring bushings just don't last very long, as in only a couple thousand miles.
You might also consider installing a stronger axle instead of a cross-brace. You can order a 5-lug axle with a larger diameter 3" tube so you can keep your existing wheels. If you turn a sharp corner, stop and get out and look at your axles, one pair of wheels will be substantially off-camber due to bending of the axle. Our TT has a 6800 lb GVWR and we have 5200 lb axles instead of OEM 3500 lbs. Huge improvement.
Adding gussets directly above the spring hangers will help to reduce flexing of the lower web of an I-beam. The photos below are from a previous 29' TT we took into a frame shop. Notice the distortion in the I-beam due to the spring hangers constantly flexing left/right. This is after only 2K miles from Indiana to the dealer on the west coast. Eventually, this would probably lead to fatigue cracks in the frame. The spring hangers which were bent to one side by around 5/8" out of plumb.
Personally I wouldn't just install a cross-brace only. Besides adding gussets, boxing in the spring hangers would help reduce the side-side flexing. Any welding should be done by a certified welder who knows what he/she is doing. But like the frame & axle shop said about our previous TT, no amount of upgrading to the weak frames will make it like it ought to have been in the first place at the factory.
Maybe install stiffer springs too. To go even further, install shock absorbers - the improvement is amazing. Everything you can do to reduce movement of the trailer "box" relative to the ground will help. Even upgrading from LRC to LRD tires will help.