I'm assuming acetaminophen and ibuprofen are not banned medications.  If your dogs are a little sore and stiff after a difficult run, why not administer small doses of those?  Certainly humans eat them like candy for few hours of relief of their aches and pains.   I seriously doubt Seavey gave his dogs Ultram.  Too much is at stake to do something so stupid when he could get the same effect with over-the-counter analgesics.