I have a better plan (added to my Todo): I'll use my recent scraper, and remove any user who creates a new post. That should work for most unbanned users.
This is now implemented. It was a lot easier than I thought (sorry for waiting this long) 
The details
1. Every day, I make a list of all users who made a post. I miss some, but scrape more than 99% of all posts.
2. I add all new bans from modlog to the Banned users list.
3. I remove all users who posted the previous day from the list.
This means that someone who posted yesterday and was banned today doesn't show up yet. Modlog shows data for the past 7 days, so this user will be added a day after he stopped posting.
If a ban is changed into a temporary ban, I can only know about it when the user can post again. He'll then be removed from the list at the next update.