a) Your original post states the Aryas experience "appearances that are the results of ignorance and karma during post-meditation." I assume that although these arise, the Aryas are not deluded by them, unlike ordinary beings. I.e., they experience them as "dependently-arisen mere appearance" and this is what is meant by the "mere relative."
b) Your subsequent comments suggest "mere relative" may be somewhat comparable to the "pure dependent nature." I don't have my NB sourcebook handy but "pure dependent nature" indicates the appearances of the higher stages of the path, e.g., the pure lands, etc. Would these qualify as karmic visions? Also, how would this fit with the Bodhisattva vow and the idea of being reborn in any of the six realms of samsara?
Regarding a), I'm glad you addressed this, Mike. I think you hit the nail on the head with your suggested description of why the mere relative is called as such. Appearances arisen from ignorance manifest for realized beings in post-meditation, but the beings do not believe that they are real. The Tibetan phrase that describes this perceptive state is snang la ma zhen pa, perceiving but not clinging, fixating, reifying, or getting sucked in.
The topic you raised in b) is very interesting to consider in a Middle Way context. The Karmapa, in his commentary, doesn't make much mention of pure realms and kāyas, etc. In one telling line, he speaks of how the purification of clinging will eventually lead to the purification of appearances, but he doesn't really describe what that purification would "look" like. A safe reading of the Consequentialist system would be to say that all pure realms, etc., are appearances for others, but the Followers of the Middle Way (i.e. the noble ones) are free from any positions (and, it would seem, perceptions) of any existence, nonexistence, etc. of appearances. In terms of the benefit of others, I think the Consequentialist explanation would accord with the general Mahāyāna: that the bodhisattvas, on the level of what is commonly accepted by others, intentionally take birth in saṃsāra to perform the benefit of others. Any display of pure realms, etc., would be an extension of that altruistic vision.
I might have more to say about the purification of appearances later...