On many mainstream steels, the finish you get from the medium Spyderco will be fairly close to what you'll get from the EF DMT. The DMT EF might still be just a tad coarser, especially on more wear-resistant steels (because the diamond will cut more deeply than the ceramic on those). If you're already favoring the finish you get from the Spyderco medium on your DoubleStuff hone, you might get away with using just the XC, C and F DMT's prior to using the medium Spyderco.
On the other hand, if you're using high-wear steels like S30V, with heavy vanadium carbide content, I'd recommend the finer diamond hones over the ceramics, because the diamond will cut the carbides much more efficiently and consistently; you'll notice this more as you go finer in finish, when the size of the carbides begin to impede less-hard abrasives at smaller effective grit (such as the alumina in the ceramics). It gets more difficult to thin or refine the 2-4µ vanadium carbides (in S30V) with less-hard abrasives of similarly small size. At coarser grits above 5-10µ and larger, the carbides will just be 'scooped out' of the matrix steel and not refined so much anyway; in which case, using diamond isn't as necessary for honing at that slightly coarser finish. The DMT EF is 9µ, and that's right at the threshold where you'll begin to notice much better performance on more wear-resistant steels, as compared to ceramics.
In the short term, you might try out the new Dia-Sharp hones and see how they finish through the EF, and following with your existing DoubleStuff hone's medium side. You might figure out you won't need the additional Spyderco medium bench stone so much, if you don't see much improvement going from the EF DMT to your DoubleStuff's medium side.
(I have the Medium and Fine Spyderco bench stones, and have almost never used them, BTW.)
David