Geez, you ask some hard questions.
There is, to my knowledge, no diff in taper amongst all of the campy four flat, square taper bottom brackets. I just went to the garage and verified that a strada crank will work with a snobbity record carbon bottom bracket axle. If everything clears and snugs up, yer good to go. Else, some ham-fisted bike shop guerilla overtightened the fixing bolts and mashed out the holes in the crankarms (horrors!)