With 4 picks, I can get the skeleton of a C13 ( b7 1 3 6 ). But you're right - no 9th sound. Also, with the b7 on the bottom, 7th chord inversions using the high strings as I'd like to do, don't sound all that good. I thought I could put the b7 in the middle, but after some experimenting, I realized that would negatively impact playability. I'm considering moving it to the top string, but doing so would likely require a different nut.
@piebaldpython has a Bb C E G A C E D tuning (the D is lower-toned than the E), and thus gets a 9th. But I'm not prepared to give up having a full major triad at the top because so many of the licks I hear in my head need it. I'll definitely do a bit more experimenting before I settle on a tuning. The Chrome Planet Wave tuning machines make changing strings so simple that it's just a matter of how many strings I'm willing to trash in order to try things out.