Esslinger (the expert for Physconia) agrees with you:

“lower surface pale throughout (small specimens) or darkening centrally (in larger well-developed specimens), the lobe ends distinctly whitish and ecorticate, usually with distinctive blackish striations developing and becoming more numerous inward, these eventually coalescing to form a poorly organized and very dull “cortex” in many but not all specimens"

There’s a photo in the Sonoran Flora (vol. I) which clearly shows nonsorediate marginal lobes in a rosette just like yours, totally blowing my half-formed theory (about sorediate outer lobes) out of the water. :)

Now I know what we’re talking about. The lower surface of tips of the lichen in question here is identical to H. neglecta in the gallery below. Again, that would point to P. perisidiosa. I discounted P. detersa due to a different general appearance and white lower lobe surface (unless you say otherwise).

I trust your C / KC test, but you still haven’t proven to my satisfaction that this can’t be P. detersa. :) I’m arguing that all of your marginal lobes have no soredia, and that this points more to P. detersa than P. perisidiosa.

As for deciding whether it has cortex below or not, the key is the texture. The cortex of Physciaceae species is a layer of densely-packed hyphae parallel to the surface. Some are long and narrow (prosoplectenchymatous), others are short and blocky (paraplectenchymatous – I didn’t come up with these terms!), but in either case the result is a shiny, smooth, plastic-like texture. (At least where not overlain by a layer of pruina or tattered dead cells, making the upper surface of Physconia appear particularly dull, for example). The medulla, by contrast, is a very loose network of thread-like hyphae with mostly open space, having a cottony or cobwebby appearance under the dissecting scope. Heterodermia is the best genus to study the feature, because it spans the entire spectrum.

H. leucomela and H. erinacea with no cortex at all

H. neglecta with a hardened but still non-corticate lower surface

H. granulosa with a technically corticate but (I think) ambiguous lower surface

H. albicans and H. speciosa with a “normal” thick shiny cortex

Unfortunately I don’t have any photos of the underside of P. perisidiosa, but it is somewhere between H. neglecta near the tips tp H. granulosa toward the center. At least the few I’ve seen. It’s much less common than the other species (P. enteroxantha, P. leucoleiptes, P. detersa, P. isidiifera).

One thing (among others) that I have to learn yet is how to figure out this question. Like you said, I should have specimen of both kinds side-by-side to figure out what it means. Unless there is a good visual comparison shown somewhere on the web.
And I did scrape some of the soredia off (inadvertently though) and tested right underneath, with no results. So everything so far points to P. perisidiosa

The primary character for P. perisidiosa is supposed to be morphological: soredia under curled-up lobe tips instead of marginal. But in very well-developed specimens (like these) even P. detersa, P. leucoleiptes and P. enteroxantha (morphologically pretty much the same) have soralia that extend around the lobe tips toward the center.

There are a few tricks worth trying, though, that might help. P. perisidiosa is essentially decorticate underneath, or at least only vaguely semi-corticate, especially near the tips. This is at least partially because the lower surface is eroding into soredia toward the tips. If you have samples of both P. perisidiosa and any of the others, compare them; it is really is distinctive when seen side-by-side.

Also, the way to get around the annoying dark-soredia-obscuring-the-spot-test problem is to carefully scrape away the soredia to expose bare medulla immediately beneath and adjacent to soralia, then test that instead of the soredia. In true P. leucoleiptes, with a great deal of patience, you can remove the cortex from a large patch of a lobe near a soralium, exposing medulla both near and distant from the soralium. If you apply the C and KC very sparingly, you will see it clearly react only near the soralium but not in the center of the lobe. Only when I see this clearly do I consider it an unambiguous identification (and not P. enteroxantha with weak concentration of secalonic acid A). It is worth the extra effort of doing the KC test instead of the C test, because it is much stronger and more reliable.

This could well be P. perisidiosa. I don’t yet have rock-dwelling P. perisidiosa, but I do have P. leucoleiptes, and the general appearance suggests the latter. However, I didn’t observe K+ yellow-orange (or KC+ for that matter). But part of the problem is – the soredia is dingy-brown (mostly), where it’s hard to observe color change, if any. On the other hand, there are tiny patches of whitish soredia, and those didn’t react either, suggesting P. perisidiosa. The center of thallus is covered with green-colored isidia-looking soredia, that suggests (I think) P. perisidiosa too. I accept any suggestions…