Jeep 'death wobble'

[LeftmostAardvark]

I've just picked up a 2.8 crd jeep Cherokee and it turns out it suffers from a death wobble, which from a bit of research is a common problem. I need to fix it - it isn't the tracking and balancing as I've had that done. Any suggestions about what to try next? There's a suspension repair kit on eBay which might work - but it's a couple of hundred quid with no guarantees of it actually fixing the problem. Fortunately I've got a good local garage with experience of jeeps so can start down that route but part of me is now thinking complete suspension overhaul with aftermarket kit (not lift, just decent branded stuff). Thoughts?