I have asked around and posted on the ebay Glass Board too. Some have seen items in the same pattern before, but nobody knows for sure who made them or who the H
mark belongs to. Homeco
was one suggestion, but they always used their full name as far as I know and Lancaster\Colony\Indiana Glass made most, if not all of their glass items.
Hocking came up again, but everyone who has a book on the subject or just a book on Milk Glass says the item is not covered in their books and there is no mention of Hocking using any mark on their glass, until they merged with Anchor and the Anchor-Hocking mark began being used, but not on everything.
Everyone agrees that it's definitely not Heisey's, not Imperial, Westmoreland, Fenton etc., because those companies did hand made glass and your piece appears to have been machine made, like something Anchor-Hocking, Indiana Glass, Jeannette or one of those makers would have done.
Ignoring the H
; I have a feeling it may possibly be a Hocking item, but maybe an earlier, unknown, undocumented sleeper item and mark or something like that. The reason for my mere
speculation is the slightly translucent, less opaque type of white glass used and another detail I have only seen on a Anchor-Hocking milk glass item of a different pattern.
I found a link to a Anchor-Hocking museum and thought maybe you might wish to contact them and see what they can tell youhttp://www.anchorhockingmuseum.com/History%20of%20Anchor%20Hocking.html
Wish I had more than that to offer, Mike