Please take a look at attached (lots of guesses - may not be fully correct).
Promotion seems simple, but brings together many configuration elements - need to understand each very well.
During Promotion Request creation, the Request object has not yet been created, so the wizard has to reach into the lifecycle, team template if used, context team, etc. and present participants with some limitations. For some cases, we have chosen instead to ignore this part of the create wizard and instead send the creator of the request the first assignment, with the Setup Participants UI - specifically to have them confirm / select participants. At this point, the request already exists, a Team instance has been created, and all seems to work much more smoothly (at the expense of an additional assignment).
Note: One major potential gotcha is that if you have users select approvers using the wizard, "The Organization" is one of the available picks. Selecting this is way too easy - result is that every single user in the organization gets an approve assignment!!!
To understand this, I had to methodically go thru some exercises of manipulating the Team Template and Context Team - and trying creating in context with various context teams.
Can discuss if you like.