Julian Cope presents Head Heritage

I don't know the details of why the proposal foundered but a couple of bits from what EH said about them in 2002 (second post down in this thread) -

1. “Many of the proposals will answer questions which have been set out in the recently published Avebury WHS Research Agenda.”

2. There's a concern it might “create a precedent for the rest of Avebury, Stonehenge and possibly other Neolithic WHS such as Neolithic Orkney.

So that suggests
(1.) any renewed call won't get far unless it involves achieving a set research aim rather than simply an assertion that the stone should be raised because it's currently buried.

(2.) In addition if people approach them hinting they'd like it to be the first of many that won't help the case either.

I have to say if that IS how EH and UNESCO are looking at it I rather agree with them. I can't get away from the conviction it isn't our generation's monument and, like tenants of a house, we're only entitled to make small changes during our all-too-short stewardship, not big rebuilding projects.