A few observations...
The mashbill for HH wheater seems to be in question as of the latest version of the tree (
http://www.straightbourbon.com/forum...l=1#post285944) but 5% barley would be extraordinarily low and my money would be against it being so - that's not much more than the bare minimum to convert all the starches in the mash. If 5% barley is truly the case, this could explain some of the difference in mouth feel (see: single malts with thick mouthfeels even at lower proofs.)
BT enters their wheater into the barrel at 114 proof. Don't know whether HH does the same, but I think this is probably one of the biggest influences on mouthfeel. People who have had a lot of dusties talk about the same sort of mouthfeel in older bottles - from the time when entry proofs were lower.
I feel like I can be pretty confident in saying that HH is using the same yeast for their wheater as for everything else - Larceny has a very noticeable HH yeast character. I bet BT does the same. I'm sure there's someone here who can tell us that for sure.