Magnetization and static charge are two different things, even though both result in an attractive force between two objects. But don’t expect a demag to have any effect on an existing static charge, except where the charge might jump from the object to the demag-er, just by chance and proximity. (In response to Elliot's post.)
Mijostyn, Besides the fact that paper and vinyl may be at opposite ends of a tribo-electric chart, what is the basis for your hypothesis that the charge is ping-ponging between them? Have you experimented with an LP from which the paper label was carefully removed? That might be useful.
In the white paper on static charge vis LPs, published in the 80s, Shure Corporation scientists pointed out that if you remove the charge from the surface of an LP sitting on a platter, the reverse side, which sits against the platter, will retain whatever charge it had a priori. As soon as you remove the LP from the platter, any residual charge on the non-playing surface will re-distribute itself evenly over both surfaces. I think that rapid process of charge re-distribution is what sometimes one hears when removing an LP from a platter, as a faint tinkly sound.