On the Constatine coin it really looks to me like an unopened umbrella.
On a more serious note, while reading your description, I couldn't help thinking of the bundles of sticks carried during the Republic (fasces?). What happened to them after the time of Augustus? Could there have been some type staff that ceremonially replaced them?
Another thought is that it is a scepter. All the depictions in Imperial Coinage of scepters I can think of are taller than a man but that doesn't mean much. During visits to Armories and Treasuries around Europe and the UK, I have seen scepters of all different sizes.