Any suggestions for very shallow, small-footprint, attractive walnut(?) subs that could sit directly in front of the KHorns, and that would add noticeable, worthwhile bass?
Disclosure: I am NOT to be considered any kind of expert (nor "vaguely knowledgeable" on subwoofers)
That said, your operative word here is 'worthwhile". In my opinion, the answer is NO (given your criteria...small footprint, shallow.
My thinking is this. You have Khorns. VERY articulate bass but not the deepest. If you mate them with some dynamic driver subwoofer, it's going to give you some "mush-a-boom" when it's doing its thing. I once heard the KP-600's outdoors. I had previously heard them INdoors.... when they were indoors, I was gobsmacked at how the hairs on my arms were vibrating. When I heard them outside, a bit louder.... I felt I could hear the blubber of the two (18" I think) direct radiator subs that were under each stack. The rest of the speaker was horn loaded.
My thoughts are you need to start from the bottom-up. You want horn loaded subwoofer (which means it's going to be big) horn woofer, blah blah.... if you have to go away from horns, then you can do that higher up because it's the lack of distortion that the horn brings you......what distorts the most? Yep, bass driver, or sub driver. So that is what benefits the most by being horn loaded.
The first 10'ish years of my owning LaScalas, I didn't know subs existed. Finally, maybe 1990, I learned about them and started looking around.
NOTHING I heard at that time (and I understand things have evolved over the last 30 years).... but nothing I heard at that time would:
1. KEEP UP with the LaScalas (same issue you'd have with Khorns with traditional subs of that smaller size)
2. As articulate as the LaScala (same issue you'd have with Khorns if you used dynamic radiators verses horns)
So, my opinion which is nothing more than that.... "if you want to do it right" the only way to do it is with a horn loaded sub and there's no way that's going to be small, WAF acceptable, inexpensive, blah blah blah"
Or, I could just circle back to your question and say "no" without all the color commentary!
Good news is, you COULD put many different subs in front of your Khorns! so you win on that question!!!