Pipeline Not Transferring Ownership Properly

It sounds like you've created an unfortunate loop issue. When you have Pipelines edit the Record Owner, I believe it will set that user as the Last Modified. Which will then trigger the change to the Record Owner, which will repeat until both Last Modified by and Record Owner are the same value. I would suggest setting a filter on the trigger so that it is not triggered when Last Modified by is equal to the user that owns the UserToken for the Pipeline. If that user is you, you'll probably want to look into using a service user for your Pipelines so that your work and the work done by Pipelines actions can be kept separate.