I'd keep the most expensive / points prolific booking in my name with my HH number (making sure both rooms are on the same folio, of course!) and let someone else have the pleasure of the other hotel's points - because I really don't think I'd get credit for all four under normal circumstances, and might find myself in a struggle with HH over which stay to grant points for, H or HI.

You can try... but I'm hoping others will post here with their success or lack thereof.