When I first started towing a TT.. I had/have a 73 Blazer and the TT was a 78 prowler 27'. It was a handful. No internet back then, so info wasn't easily available. I did several hitch upgrades, and got it to be just OK... By my then standards. Going faster when on good roads did make a noticeable improvement of the semi bow wave push. But ultimately a bigger truck took care of it for me.
I suspect that the OP is finding out that a 1/2 ton is a 1/2 ton no matter how many upgrades you throw at it.
I am not sure of the differences in Suburbans of that era, but suspect that there are frame and axle differences that just make the entire TV more stable. Items that are not really upgradeable.
So though it definantly seems counter intuitive, going faster will probably help, but may not be the needed fix.