Have you thought of adding a bigger premium for larger volumes?
This might go in the both directions.

I'm saying this because one can keep buying HBD on the DEX and convert that to HIVE without putting a market pressure on the HIVE price. To transfer this buying pressure on the market, the stabilizer will need to increase the premium, triggering HIVE to HBD conversions.

Buying larger amounts of HIVE through the DEX and the stabilizer will take a longer time, but it is possible.