I also think it's good that we discuss this on-chain, so I hope to see more comments.

If, in addition to ‘burning’, the aim is to stabilise prices or even increase them, I don't think it's necessary to wait for an SBD price above $1. Am I correct in assuming that the bought STEEM should be burned?

At the end , we just need to be clear about what could happen with which players. If we offer SBD on the internal market, this could have an impact on the external market if arbitrage trading works.
So let's assume that the DAO buy order causes the STEEM price to rise on the internal market. Arbitrage traders could buy STEEM cheaply externally in order to sell it internally at higher prices. This would indirectly lead to higher prices externally as well.
The decisive factor (and one that is impossible to predict) is what the traders then do with the SBD. If they are then sold externally, the external SBD price would come under pressure. Or we could see more conversions again.
The best thing to do would probably be to offer interest at the same time so that the SBD sold from the DAO is not resold.

Under the condition (also mentioned by @remlaps) that the accounts involved are controlled by the community, I would support it.