Here, in the sketch of 1634 above, it is plainly a sack of grain or “woolsack.” I believe it was later altered to include him holding a quill pen in one hand, a piece of paper in the other; but why would he write on a pillow in the first place? Directly below is the engraving published first in 1656:
And below – ah! – the bust as it appears today:
Hank Whittemore's Shakespeare Blog 
And as Richard Whalen discusses in the article you have attached, the monument may well have been or John Shakespere holding a sack of wool — not even Will holding the sack.
Yes — indeed — and I wish we knew how to prove it. But the whole history of that monument is crazy, eh? Thanks for commenting. (I have been traveling and just back here.)