Here's another method which addresses your concern about not getting the HBD right away and still prevents gaming or undesirable disincentives to convert by using a future price, by combining the conversion mechanism with a short term collateralized loan.

I'll describe it by example (for simplicity of description, the 5% fee is omitted here).

You request to convert 1000 HIVE. The most recent median price is 0.25. This is further divided by the overcollateralization ratio, say 2 (could be 3 or even higher without causing major problems, but I think 2 might be sufficient, especially if the window is reduced to 24 hours). You then receive 125 HBD immediately, as a loan. In addition, a request is made to convert your HIVE into 125 HBD, which will pay back the loan. At the end of the median window (currently 3.5 days, but maybe changed to 24 hours), let's say the median price is now 0.20. Your 125 HBD conversion requires 625 HIVE at that future price, which is kept by the blockchain and the remaining 375 HIVE collateral is returned to you.

There is some risk that if the price of HIVE falls by more than the collateralization ratio (below 0.125 in the above example with a collateralization ratio of 2), there won't be enough HIVE to repay the loan, and the blockchain could suffer a loss. However, I think short duration of the loan combined with the 5% fee is probably enough to make this an acceptable risk.