"Save Focus settings to current snapshot" would require all Focus view-controlled parameters be set for snapshot control. In this case, what you suggest would just work anyway—select Snap 1, move Focus lens, select Snap 2, move Focus lens, select Snap 3, move Focus lens, etc.
I could maybe see a "enable snapshot control of all parameters in this block" shortcut so you don't have to push-turn each knob, but I think snapshot parameter assignment might be limited to 96 or 128 (EDIT: It's 96 but Igor thinks we might be able to expand this count) parameters or something; I forget. (It's 64 in Helix/HX.) Regardless, you might run out of snapshot assignments quickly that way.