How to correct for delays in a PAM-X signal with orthogonal CDMA?
Couple of observations:


you can of course also correlate with the already pulse-shaped CDMA sequence as a whole – it's a long filter, then, but that (in AWGN) will essentially give you the basis of a maximum likelihood receiver.
Commutativity of convolution: Doesn't matter whether you pulse shape filter -> CDMA sequence filter or CDMA sequence filter -> pulse shape filter. The result is the same (and the same as if you first convolved CDMA sequence and pulse shape, and the signal then with that – see 1.)


In either case, you'd only do one synchronizer.