It took longer than I thought, but I came up with a promising approach for throwaway accounts. The bot can't use the same parameter set to accounts with only a few interactions as it does for normal accounts, without getting it either too loose for the new accounts or too strict for the old accounts. I had to make a special stricter setting for any account that only has a few interactions in its recent history.
1.3% of users have enough interaction data to judge for sure that people have problems with them, and they get banned just like before. 2% more users on top of that will trigger the stricter filter if they try to post, and get a polite message that they need to interact more before they can participate. 97% of users don't need to worry about any of this, just like before.
I think that approach will work. It's not done yet but I have the parameters in place for it. I think the bot is doing a good job. I was expecting it to get it wrong a few times, and I have found a couple of users it made mistakes on, but it's doing better than I thought it would.