Based on the SCSW, and some additional research, I am now positive that the regular 10-4 had a tapered, not a heavy barrel. The 10-4 was made for only a few months before the change to the 10-5, so model collectors of the 10 series value it higher than run-of-the-mill dash versions.

So if you are looking at a heavy barrel gun marked 10-4, it was either some special order or is mis-marked. Or as Alan suggests, reassembled