Hoping I could get some advise. I recently got a sapphire cosworth RWD and it runs fine with no knocks or bangs but at around 65mph+ it seems to be vibrating a lot from the rear. At first j thought it may be the wheel balancing but thats been done and it's still there. I then checked for play on the drive shafts and 1 has slight play around 1mm on the Diff side.
It goes up and down around 1mm inside the diff.
There was also what looks like grease marks over the drive shaft boot where it looks like the boot has been leaking while spinning.

Could this be the cause of the vibration and if not what else can I do to diagnose ?

Thanks is in advance.