I actually wanted to graft on this tree Kaunching and Smyrna to have few varieties on one tree. Do you know anything about how Kaunching or Smyrna are doing in SoCal climate?
I'm pretty sure Karp's Sweet is probably a better variety than Kaunching or Smyrna (not that those two are bad varieties).
Also I believe that Karp's Sweet probably has a lower chill requirement than other quince varieties (though I'm not certain about this), so other varieties would probably do worse in your climate. Considering where you live, I would not bother trying to graft on any other quince varieties.
In a warm climate with plenty of heat, Karp's Sweet is probably going to be the best you will get, I would think.
I also would like to see a photo of actual Kaunching's fruit to know more about a shape. Not to many actual pictures of it in internet. I would really appreciate if someone would show it. As far as I know Kaunching is another variety that is good to eat raw.
This is just from my memory, but from the research I did in the past it seemed like Kaunching was one of the good more edible varieties, but probably wasn't quite as good for raw eating as Crimea, Kuganskaya, and Aromatnaya.
(I mean all four varieties are probably pretty close in terms of quality for eating raw, it's just that out of those four Kaunching would come in last place)
I actually saw a bunch of Kaunching trees for sale at my local nursery a year or two ago (and was surprised because that's not a common variety) but didn't get one because I thought the two varieties I already had were probably a little bit better.
It is of course possible I could be wrong about all this, but you just asked my thoughts and opinion.