Wasn't HBP dug extensively in the late 1970s by Sheffield based cavers, many associated with the Cave Projects Group? There might be something in one of the SUSS journals - or did the CPG ever produce a journal of its own?
I seem to remember a shaft being sunk for a considerable distance without success but it may have (been?) filled in again since, partially or fully.
Incidentally the Snuffit Pot risings are pretty sensitive. We tried to obtain permission from the landowner for a dig a year or so ago (they're both well choked) but, although he wasn't against the idea, he'd just started a fish conservation programme in that part of the Skirfare and asked us not to interfere. He's a grand bloke and he suggested we approach him again in a few years time. So we complied with his wishes and kicked the project into the proverbial long grass. (It was the late Harry Long who kindly made the introduction for us.)