While I was looking for things to do for our trip to the Grand Canyon this month, I came across this tour company, maybe their Grand Canyon Safari and Rim walk tour is something like you are looking for? http://www.grandcanyonjeeptours.com/tour.htm
If you google Grand Canyon Jeep tours there are lots of companies that depart from the town just outside the park.
Looking at the map - http://www.grandcanyonjeeptours.com/map2.htm - it appears that the trip is on the main park roads, easily accessible, except for the part to the rim . . . that's thru the national forest.
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