What Andrew S said.
Also, an old "Chet" trick, only fret the strings you need to make passing contact with. Fretting all the notes in say a C chord when you only need to be making contact with the high B and E, will slow your fretting hand down. Keep the finger height as you switch from position to position (with your fretting hand) at the absolutely minimum height to just clear the strings. THIS, also takes practise, and there is a tendancy to want to flail your fingers over the strings, but the more height of the fingers rising and pressing down on the strings, the more it will slow you down. (Forget anything you've ever seen electric players do. The majority are dealing with feather light action and string gage, where only the slightest pressure will fret the notes.)

Ironically I too have been working on Beaumont Rag. I based my arrangement on the version that Doc and Chet did together on the "Doc and Chet" album (1979). Thing is, my convulated mind likes to "make trouble" for myself. I took what was a straight flat picking arrangement and turned it into a fingerpicking arrangement, with the index and middle playing all the flat picked leads while the thumb keeps an alternating bass going, as well as using Doc's flatpicking fills as two fingered flat picking breaks. It was great fun, a great exercise in dexterity as well as logic to make it work. I cannot however play this arrangement at any kind of lightning tempo, because there are a lot of notes to be covered and a lot of hand movement with the left hand. Best I can do is a medium tempo at around 110 bps. Still perfecting it, but plan to record it soon and work it into a medley with Liz Cotten's "Babe Ain't No Lie"...and use Beaumont as sort of a "C" part or alternate bridge section to the Cotten tune.