" I wonder how to become a bit more ashured that some foolishness from over a quarter of a centry ago won't come back to haunt me."

I'd apply NOW for an RABC permit.  (and yes, you still have to have a regular passport for re-entering US - if you don't already have one, apply for one now - it can take up to a couple of months).  If you get the RABC permit, fine and dandy - plan an entry from the south thru Prairie Portage or Cache Bay and loop back to your cycle, which is at one of the outfitters based on Moose Lake or Sag - no shuttle involved at all.  Alternatively, start the same, but finish up North and make arrangements with Canadian outfitter to bring you back to US - as long as you have your Passport, no issues crossing the border from N to S - its only entering Canada that may be a problem.

Plan B - do your research (just google for Entering Canada with a DUI on licence or something that general, and you'll find lots of hits)  Canada Customs - and find the info about buying your way in - I think its $150 to forgive you your sins.  You have to fill out some forms at the border and pay your penance - BUT - there is no absolute guarantee that you will be allowed to cross the border in either direction - it is always up to the crossing guards, no matter which way you are going.