Hive sent to the DHF is instantly converted, so when the stabilizer sends Hive to the DHF, this becomes HBD immediately. Unfortunately, due to specification change to the proposal system, only 1% of this HBD is immediately available to fund proposals.
Also, the initial Hive supplied to the DHF was hardcoded to be slowly converted to HBD, and the witnesses don't have control over this rate.
Despite all that, the amount of HBD available to fund the stabilizer proposals is increasing at a reasonably fast rate.