Civimember: token for membership end date not working
I'll call this an answer, only because it worked. I discovered this link after googling around. civicrm.org/extensions/nzcofuzioncivitoken
After installing the extension, my Expiration Template now contains:


  Your membership is paid thru: {latestcurrentmembership.allend_date}
  
  Member since: {latestcurrentmembership.alljoin_date}


Since this seems a practical necessity for Membership-related Scheduled Reminders, I updated the documentation for Membership > Renewals to point to this extension for others who wish to associate membership information to the contact in the reminder.