I think sending back to the DAO is fine. If stakeholders want coins from the DAO burned, they can vote a burn proposal. As you say, it is essentially de-printed and out of circulation in any case.

Sending coins back to the DAO is not inflationary pressure. It is that PLUS payouts from the DAO getting voted which could be inflationary.

The reason I'm not a huge fan of automatically burning the rewards here is that it makes a vote for this proposal into a vote to stabilize HBD and also a vote to burn funds from the DAO. To me those ought to be separate.

If the DAO contractor doesn't do the converting, someone else will, and they won't burn the resulting HIVE either. At least the DAO contractor will send them back to the DAO, getting them out of direct circulation.

Finally, your suggestion as written wouldn't actually help the peg significantly. If the price of HDB is too low, you need to buy HBD on the market and/or remove HBD from public circulation, but your suggestion does neither. It takes HBD from the DAO and effectively burns that, which doesn't affect the circulation or market price in any direct way.

I actually agree with only paying interest on savings. It makes interest into a form of staking rewards (though the stake period is short, 3 days, it is not zero). And if that encouraged exchanges to put their HBD in savings (maybe paying out to customers as "staked" returns, maybe not) that would be a positive in terms of being protective against exchange hacks.