I would have to veto this idea. I don't think running a two tier game would work too well. It would be like running two completely unrelated campaigns, given that the background info from the lower level characters would not be in sync with the plot line faced by the higher level characters.
Additionally, from a story perspective, there wouldn't really be a satisfying end to things for your lower level group, or a satisfying beginning to things for your higher level group.
Your higher level group would also be uncovering surprises (especially as far as NPC's are concerned) that would ruin things for your lower level group.
Are your players determined to stick with their high level characters? If they are I would suggest not rnning the SCAP for levels 11-20 only, but running some other campaign instead (perhaps the Shadows of Istivin arc).
If they're ok with rolling up new characters I would defenitely suggest playing the SCAP from start to finish.
I'd try both campaigns at first - starting SCAP with new characters and finding alternative adventures for the high level group and over time see which group your players find themselves prefering to play, and go with that.
As has been said, it wouldn't work to run the two groups concurrent because of how the plot is laid out without a LOT of work. Having the lower level group working for the higher level only works if you run it consecutive (1-10 doing their bit and then retiring while 11-20 takes over). You could have a little interaction with your higher group as NPCs advising the lower groups, but that's about it.
I ran it from the Dungeon issues, so I don't know how it's laid out in the hardback. In the magazine, the plot was unfolding layer by layer even for the DM with each adventure. If you REALLY want to do this, the only way I can see it happening is if you purchase and read through the entire adventure so you know the story, then go back and rewrite the adventures yourself with regards to how the main plot is unfolded for the players.