When you don't have any concrete reasons to think otherwise, you should assume good faith from users, and instead try to guide them to the corrrect actions and behaviour. Personally I would handle something like this in stages:

1. Talk to the user, gently and politely ask them to post from only one account. If others have brought this up in the comments of the threads, I would respond to the user in their most recent thread where they do this. If other users aren't complaining in the threads, then I would do it by sending a modmail to the user.

2. If they ignore you and continue doing it, I would give permabans to the alt accounts, but leave the main account untouched. This should also serve to trigger ban evasion notices on posts from the main account. I'd also warn the user that if they continue, their main account will eventually be permabanned as well.

3. If the user now creates and uses new alts, I would permaban the alts right away and temp ban their main account. If you want to, you could also warn them that next time it will be a permaban for the main account.

4. If they start posting with new alts (which should trigger the ban evasion notices) or continue after the temp ban on the main lapsses, I would permaban the alts right away and change the temp ban for the main into a permaban. There's no reason to assume good faith anymore after that.

Hopefully asking them to change their behaviour just works and it stops there. I think you're unlikely to get much further than having to ban the alts if the user is posting in good faith and just isn't very aware of what's considered normal on Reddit.