Toniniopsis/ Thalloidima?

Since nobody else has made any suggestions, I am going to give a very tentative gut reaction. The habitat and the appearance of the convex areoles put me in mind of Trapelia glebulosa s. lat. This ought to be ruled out by your report of a lack of C reaction but the C+ red of Trapelia species is often missed, especially if performed in the field. With moist material in the field the reaction is often completely inapparent. As with all spot reactions, the only truly reliable way is frugal application of strong fresh reagent to dry material under a dissecting ‘microscope. There is something rather distinctive about Trapelia and a few other genera and that is the way the photobiont cells divide. In Fuscidea, Trapelia, Trapeliopsis (and a special case in Micarea) the algal cells divide by binary fission rather than forming a cluster of daughter cells before division.

Here is a drawing of the algal cells and host hyphae in Trapelia; the binary fission producing a paired or quad appearance.

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Here is a section of Fuscidea lightfootii thallus.

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For comparison here is the formation of a cluster of daughter cells as seen in Caloplaca obscurella.

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So, if you want to pursue this, you might want to look at the cell division of the photobiont to strengthen or disprove my suggestion. Of course I have taken photos of particularly convincing examples of binary fission and of division into clusters of daughter cells and it isn’t always so easy to decide which you have but a careful examination of a portion of thallus, mounted in K to relax the structure, usually allows one to decide between these two types of division.

I’m not quite sure what to say about the algal cells. You are probably right but the ones that are most unambiguously dividing by binary fission don’t have any associated hyphae attached to them. Any such hyphae have either come loose on squashing or one also has to be careful because many lichen thalli have some unassociated algae growing on them, often Chlorella type which divides by binary fission.

I think this lichen will have to remain unnamed for the moment since we don’t have any apothecia, no C reaction has been detected and I can’t be certain about the photobiont. There have been many instances where I have found mysteries in churchyards which I couldn’t name when I first encountered them. A fair proportion of them eventually became resolved one way or another. I will keep your lichen in mind just in case I have a flash of inspiration with a different/better suggestion.