Well, I don't see a problem with leaving the s/n as the dominant one. I know using the s/n for the c/n bothers some people, and if it has never been civil registered it should use the c/n. But if the s/n was used for registration, it actually helps locate the aircraft. I have found many of my birds by searching the s/n and would never have even known the c/n. Since the FAA shows the s/n in place of the c/n, I'd just go with it.
One advantage of using the s/n over the c/n, is that many c/ns will be the same because each company has their own numbers. But s/ns are only applied once. There is an anomaly which will give the same aircraft multiple s/ns - for example, when aircraft are traded in service. A plane with a Navy BuNo transferred to the USAF will be re-serialed in the AF system, and vice versa. I can't remember which bird it is off the top of my head, but I've seen one plane (C-130? HU-16?) which started with a USAF number, was transferred to the Navy and picked up a 6-digit BuNo, and ended up with the USCG with a 4-digit number!