The engines with the 357 cam do have a lopey , cammy idle when warm, or at least mine sure does.
Ive no prior experience with these bikes and at first thought the idle needed improvement, although its actually a strong idle, no dieing.
Then I listened carefully to half a dozen or so YouTube videos of running post 61 Super Rockets.
Every bike had the same idle as mine.
Now I like the sound, it's a signature BSA 357 idle.
These are HHC bikes afterall.
I haven't given a good listen to the earlier HHC engines with a bit lower compression and 356 cam. I suspect they may have a similar idle.
I've also noticed that the idle of this SR is dead smooth when cold. I think this is because I lift the slide ever so little to maintain running when cold.
Later on when the engine is warm and the slide is dropped onto the idle stop, the brup brup idle comes in.
So the cammy sounding idle may be down to air /fuel mixture idiosyncrasies of the BSA A10 inlet tract, not the cams and compression.
Edit- here is an early HHC in a 57 Road Rocket. The idle sounds very much like my 63 SR.
https://m.youtube.com/watch?v=oQIoP_iNDwQGlen