Scratching some quick equations on the back of the proverbial envelope...
According to Sidgwick (p.50) the Cassini division has a width of 0.5". If this corresponds to a width of 4,500 km as mentioned above, then the Enke division at 350 km has an apparent width of only about 0.04". Sidgwick (pg. 50) also states that the visibility of a "single dark line on light ground" (with Cassini as an example of such), is on average 1/5 of the Raleigh limit (R'), with values quoted up to 1/15 of R' in the case of exceptional observers and/or equipment.
At 1/5 R', a scope in excess of 20 inches aperture would be required to see the division.
At 1/15 R', a scope of nearly 8 inches would be required to see the division.
This would, of course, be valid *if* the Encke Division was sitting all by itself in the middle of a white expanse with no other detail near it. It isn't. Again, the problem is that the Encke division sits in a brightness falloff (a more greyish portion of the A-ring) and is simply too close to the outer edge of the A-ring to be easily resolved in the diffraction sense. At *best*, it lies only 0.5 arc seconds from the edge (and much of the time, it isn't even that far in angle from the edge). At minimum one needs an aperture that can do that (ie: one larger than about 9.12 inches), and certainly a larger aperture would have a better chance of detecting this feature. In fact, the minimum aperture to see the Cassini Division is also constrained more by this resolution limit (2.4 arc seconds from the outer edge of the A-ring for the case of the Cassini Division) than by the width of the division itself. Clear skies to you.