Participant#advance and PBS transitions

I'll separate these later.  For now, consider this a preview of a work-in-progress; it should _not_ be merged as-is.  Comments strongly recommended.

References:

https://code.bioinformatics.northwestern.edu/issues/issues/show/3128
https://code.bioinformatics.northwestern.edu/issues/issues/show/2815
https://code.bioinformatics.northwestern.edu/issues/issues/show/2607