If it were me, I would take it apart. Before you decide whether to dismantle or clean in place, take a look here for full instructions complete with pictures. After looking over this webpage you'll be in a better position to decide whether you want to take this on.
https://pungoliving.home.blog/2020/0...balance-wheel/
The man who runs this site, Lee, is a retired engineer who regularly takes vintage sewing machines apart, restores all the parts and puts them back together. He is someone who is happy to share his knowledge. An altogether extraordinary individual. If you can't get the 201 up and running with the suggestions you've seen here, it can't hurt to send Lee a message and see if he has any suggestions.
Lee has also posted a step-by-step "record" (I hesitate to say "instructions" but it's close to a that) showing a full restoration of a 201 here:
https://pungoliving.home.blog/2019/1...-singer-201-2/