My first thought was that maybe it's the base ring being too tight, but the latter device kind of rules that one out.
I also thought that - just maybe - I'm using too small of a cage, but now I have two versions of the Looker (I got the parts interchangeable so it's kind of cool),both snug length but other with a slightly bigger diameter and base ring as well, and it's still appearing.
The swelling / edema would start appearing in 24 hrs and get bigger if device usage is continued for several days. Taking the cage off makes the swelling disappear in a few hours.
The devices are all comfortable and I'm having the foreskin back 24/7 with or without a cage. I have a 6mm PA but that would be unrelated to the issue since the same happened even before getting the piercing.
Maybe this would better go to a topic of its own, but I've personally just been kind of trying to solve this puzzle by myself.. I realise something similar at least has been discussed before, and the solution seems to have involved a doctor, a knife and removal of certain pieces of very personal skin. Any other experiences are highly appreciated!

Anyways, my better half has gotten more serious about keeping her property caged so now I'm enjoying the ride and seeing if it's just a matter of training. I hope! Meanwhile, having to get out for the night every few days isn't that bad a thing either, considering there's an elevated chance of getting some attention.