If I understand you correctly, sounds like it won't pitch-rotate and dead-hooks ?
Sounds like you've thrown some tweaks at it but it's not hitting the back tires enough or inconsistently ?
I assume it leaves & goes straight ?
Converters are known entities & behaving properly ?
I don't recall if it's a ladder, 4-link or leaf car, but I'd snoop around the rear suspension area...including bushings, heim joints, spring rates still good...