In part for similar reasons I would like to see some of the fee moved to the HBD->HIVE conversion.

Well, if there is a fee on the HBD->Hive conversion, then HBD is no longer always convertible (by the blockchain itself) for $1 worth of Hive, so that would break the solid foundation which makes HBD a secure place to hold your money. The HBD stabilizer is a very good extra, but the real security comes from knowing that the blockchain itself offers you $1 worth of Hive for each HBD you hold. These assurances are what people look for.