Can you film what's happening when the 'fault' occurs so we may see if they are indeed spinning off-centre?
Are these Commercially available DVD's or DVD-R/DVD+R/DVD-RW's etc etc?
What Player are you using?

I am not for a minute disputing you are having problems but after 30 years repairing domestic electronics I have not come across this before in a domestic DVD player, only in a PC Drive which, when Ripping CD's and having to spin at 'excessive' speeds I would experience some vibration and worst case scenarios would not be able to read the disc. Playing back at 'normal ' CD speeds it was fine but at the ripping speeds, similar to DVD speeds, it would vibrate. This was due, I think, to variances in the thickness of the Disc caused by the Ink for the Labels on some CD's. When watching these discs spin I never saw them spinning off-centre.

Some 'damping' added to the very cheap Plastic Mechanism cured the problem changing the resonant frquencies of the Mech.

Jim.