Here is my round butt Model 64 with tapered barrel. I sent it to the factory to have the barrel installed as this was never a factory configuration.
According to SCSW 4, the Model 64 was introduced in 1970 "w/tapered barrel in 4" barrel length". The heavy barrel was introduced in 1972 as the Model 64-1 in .357 Magnum for the Oklahoma Highway Patrol (which, of course, was later designated the Model 65.) The tapered barrel continued to be available until the following year, when it was dropped.