The 34 (previously the Model of 1953 Kit Gun) was built not on the I frame, but on the I frame improved.
The I frame improved incorporated the coil mainspring that is now seen on the J frames, moving away from the old I frame's leaf main spring.
The 34-1 was the introduction of the J frame, in 1960, although there are supposedly some 34-marked J frames floating around out there.