I suspect that there's a good chance that somewhere, someone has written about modal logic such that their system takes contingency as a primitive, and uses a "new" symbol for this. That, or maybe they repurpose the box and diamond, there. But this is just speculative. I've been reading more of/about a wide range of Central/South American logicians, and Spanish (IDK about Portuguese) tends to use certain punctuation marks more often than, or above those in, English. (At least, the rotated question mark shows up, bracketing entire sentences, like an unusual parenthesis over those sentences.) So maybe there's a place to start looking?
Besides all that, I do recall, though not by the author's name, a system where there was an actuality operator, and a circle was used for it. The author was not quite famous, even "for a logician/philosopher," but at least well-known enough (I think) that his notation might have found a few subscribers (among them: me).
As Bumble observes, so far your account of mere possibility is reducible to contingent falsity. It is not totally obvious that the same state of affairs obtains in the light of a definition of mere possibility as "possibly X and ~actually X." For now we can refer to necessarily merely possible objects: "possibly X and necessarily not actually X." This ends up being impossibility, and the same point can be made in a logic with no actuality operator, but only existential quantification and the flat assertion of a sentence sans a box or diamond (or whatever); still, the point seems more interesting when made in terms of an actuality operator (if only because of how the point reinforces the (apparently possible, but not indubitable) fact that actual possibility and possible actuality are relatively equivalent).