if its just demos that fail, your problem is not due to svc_clientdata.
check what changes you've made in cl_demo.c. make sure that whatever enables your higher precision aiming angles is also enabled for playing back those demos. considering you're not aiming for quake compatibility, and not even with the id demos, you should perhaps consider unconditionally sending/reading shorts for your angles in the clc_move commands, which would permit you to forgo any protocol toggles/detection.