OK, turns out this was due to erroneous entries in the Drupal settings.php file. The following entries were causing cookies to be missed by Civi:-
Others may also cause inconsistencies, such as:-
You should be able to limit the custom participant data to a specific event or event type and then it shouldn't show up in the back end for events you didn't mean it to.
This is done on the custom data itself (under "used for") rather than in the profile. Also to note, you usually only want to 'require' data inside the profile not inside the custom data set....
I've added this redirect, thanks for reporting it!
I think it's great you've made the effort to post it somewhere we can field it, and that the end result is more important than correct process - so don't fret about not posting it on issues.civicrm.org this time. Thanks for being part of the community! You did this to benefit others in your situation, ...