The easiest way to backpack for that length of a trip is to get into s.w. Colorado but that is beyond your driving time requirements.
If you want a significant backpacking loop or trip in RMNP you'll likely have to get a bit creative. The Park it seems is almost more a private preserve for the environmental scientists and wildlife biologists and a tourist spot than a place to go backpacking. Many of the old trails have been abandoned by the park and camping allowed only at certain sites and by permit. Their is also now a bear canister rule and I believe a carry out human waste rule.
That being said I have been working on an on/off trail route in the northern part of the park, this is a lesser traveled and wild area, away from the tourist buses and all that. The mostly gentle alpine tundra in the Mummy range allows one to link up different trails and put together a larger trip. I need to do more map work though to get a better idea of mileages and details.
There is also this http://bp2.trimbleoutdoors.com/ViewTrip.aspx?tripId=399192.
In the Holy Cross Wilderness you have a multi-day loop, the Cross Creek, Fall Creek loop encircling Mt. of the Holy Cross with an option to climb the mountain at the end of your trip.
I have drawn up some large loops linking together several trails in the heart of the Collegiate Peaks Wilderness with options to climb several 14ers and/or high 13ers. Portions of the CDT and CT can be/are utilized. Loops from 30-50 miles can be accomplished here.
If any of this interests you then p.m. with any specifics you are interested in.