While most people run it in the comfort of big rafts, several pairs of shoes, tables, and chairs, there is now another way: packrafts.
While this may not bring us back to the level of adventure that J. W. Powell experienced, it may be the closest other than running it one-armed.
Last year my son C. Roman, Gordy Vernon, and I managed to get a permit from the NPS to run it by hiking down Hermit and running the rapids to Havasu. It took about a week and while we missed some other big rapids both upstream (Granite etc) and down (Lava), we were plenty satiated with adventure by the time we took out.
The permit was not easy to get! We benefited from the help of Glenn "LB" Rink and others of Flagstaff and around the SW in getting the NPS to let us put in somewhere other than Lee's Ferry and take out somewhere other than Diamond Creek and run it in our 5 pound Alpackas.
We did it before I'd figured out how to shoot video on the Optio W60 but here's a slide show: