Belcher to Old Faithful - Yellowstone - Key Swap

The Bechler is spectacular but the route you describe is a logistical nightmare. Just a suggestion. Can you alter your route to enter at say, Kepler Cascades near Old Faithful and exit across the Pitchstone Plateau (interesting landscape) and come out on the South road (Phantom Fumarole)? Then you could easily hitch a ride back to your vehicle. That's one route I've used. You would still see the best of the Bechler region. Or you could exit at the Grassy lake Road along the south boundary and hitch a ride to the south entrance and then back to your vehicle. Traffic would be much lighter on the Grassy Lake Road, but eventually, especially during the summer, a pickup or whatever, will come along and give you a lift. I've done it several times with no major problems. Great area to hike.