The S360 is basically an S560 without a user-adjustable poppet spring tension. You could convert a 360 to a 560, but I'll need to check schematics.
If it were me, I wouldn't spend the money on those particular upgrade parts. You need to ask yourself, how often do I change my inhalation resistance? Maybe screw it in walking into the surf, then full out for the rest of the dive. Just maybe you might want to screw it in a little if air density made the venturi action too forceful on a really deep dive. But if you're diving that deep that often, I'd get a slightly more robust reg anyway (G260).
IMHO, the S360 is a great reg that, if properly tuned, breathes no differently than most 560's, 600's or 620's. The extra knob of the 560 is a nice to have, but not commonly useful.
More important, just like the S560, S600 and S620, the S360 already has the user-adjustable VIVA vane, which is the better adjustment for preventing inadvertent freeflow before a dive anyway.
I'd spend the money to upgrade the S360 to an S560 as long as the upgrade is less than a $100. I wouldn't buy the S360 thinking that I'd just turn around and upgrade it to an S560, that would be silly and I should have bought an S560 from the beginning. I'd upgrade to an S360 if at some time later after I bought I thought that I really wanted the adjustment knob (I would want it for sure) and do it if it is less than $100 to do it. For ME, the ability to adjust my regulator according to the circumstance I am diving in is very important for me for sure. The S360/S560 are excellent second stages for recreational diving depths in >10C waters.
Now there is a much better second stage that is out from SP, the C370. It has the two adjustments, little smaller profile and breaths awesome for the recreational diver (down to 40 meters). We just got three units (with MK17) for use in our dive school for the upper level courses.