I think you have everything you need to tow your 76 Sovereign
You mention the ride height of the trailer has been increased significantly, maybe with new axles. Good axles are important as your stiffly sprung truck will transfer some bumps back to the trailer. I tow with a F-350 and haven't had any problems.
So the first job is determining the ball height that will allow the hitched up trailer to follow the truck on the level to a slightly nose down attitude. Make that adjustment first.
You mention you have an equalizer hitch with 1000 pound bars. It's a good hitch. The equalizer bars rest on friction pads with a considerable down force that provides some sway control. You need to set the angle of your hitch head to load up the bars. I'd just follow the factory set up procedure even though your truck may not notice any weight distribution. But there will be some and that's what provides the sway control through the loaded bars. I think equalizer likes their bars parallel with the A frame member.
I had a bit of problems with my equalizer as I could not keep the bar mounts from moving. I ended up shimming the bar mounts to eliminate any clearance between the lower bolt and the frame rail. That solved my problem.