Bill Tindall, E.Tn.
It should not be hard to find some business with a 24" planer, and not any problem getting them to plane new commercial lumber.
Personally I would not go to much effort to make a case side from one board. Case sides are rarely the focal point of case goods. I might work on using such a single board for a case or table top. Frankly I think you may be more enamored by the idea of this board than the result will justify.
If you rip the board down the center you will be rejoining "V" pattern grain and it will not exactly match because you will have removed some material from ripping and jointing. And a near match is not attractive. Again personally, even if I had 10 of these boards available I would be making the 22" case side by attractively gluing two 11" boards. I strive to make the joint attractively contrasting. (see PIC for an example of a two board case side joint)