I have been in vague contact in the past with a bloke at The Property Merchant Group (the ppl who own 111 cannon street) & have just emailed him again to find out the latest.
Last time I had contact (about 8 months ago) he assured me The Stone would be moved in conjunction with the relevant authorities & would presumably be stored at the Museum of London in the interim.
All of which said on the proviso he probably thinks I'm some raving looney (see nigelswifts thread :).