On Sun, 15 Apr 2012 15:40:21 +0100, wrote:

What's the best/easiest way to remove the residue of what looks like
pretty standard contact adhesive that's left after pulling off the
vinyl and the laminate?

Angle Grinder.

Seriously I don't think there is anything that will shift it and
leave a presentable surface afterwards. Probably easier to replace
the partition with a new one or reface it.

--
Cheers
Dave.