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I think there would very soon be stability - because people would realize that the mechanism which brings down the SBD price is too strong to speculate against. At least I would think it would work like this.

I think we have to accept that all we can do is creating a mechanism which results in a peg if people react rational. For a real peg, you would have to make sure that the value at any tie is really worth exactly 1 SBD. For this to reach, there needs to be an arbitrage possibility. For example if could would have the opportunity to create new SBD at any time by paying 1 USD and to get your 1 USD back it would certainly be closely pegged to the USD. However, this is not possible and wanted I think. The only other way is to create a mechanism which is sensitive to the USD.

I think, if you would pay out the SBD part also based on its USD value as you do with steam, the price would sky rocket even more because inflation would go down massively.