I think it has to do with when the frame was made.
I have a couple K-frames that are just like your's, and a few that would be no problem. On the later ones, the machining is a different configuration under the grips, and there's more metal under there.
I assume S&W did this to make production easier, being able to cut the amount of machining, and make a frame that could be used to make either SB or RB without a separate operation other than making it round.
The serial number placement moved as well. Some S/N's would be partially obliterated by a RB conversion. On my later ones, the S/N is in a different place that would be unaffected by the conversion. Again, I think S&W simply changed how they stamped the S/N to make it more efficient. It makes sense to just have a single standard operation for stamping a S/N, rather than one for SB and one for RB.
Regardless of reason, the bottom line is the RB conversion works fine on the right frames. It would be pretty problematic on some of them though. Sounds like you have one that would not lend itself to the RB conversion easily.