I have the answer! (well it works for me anyway)
Pardon my exuberance, but I have been very much looking forward to reporting this. Like Trask and others I have been frustrated by the overdeveloped edges I was consistently seeing in all my caffenol-C developments (despite the fact that not everyone seems to experience this), and found this a debilitating defect in what would otherwise be a very nice, fun developer. But a couple weeks ago after a lot of experimenting I finally made a breakthrough!
First I should point out that I tried a lot of different things before finding a solution that worked for me. The obvious was to increase or decrease the amount of agitation. I went all the way from continuous agitation, down to stand development with no luck. I tweaked my recipe by varying the amount of soda, the coffee/vitamin-C ratio, and different dilutions, all to no avail. I experimented with different temperatures. I tried filling the tank completely, or leaving a substantial air pocket. I even tried adding spacers in the tank to immobilize the reel in the tank and limit its movement during agitation, but again the results didn't seem to change very much.
What I finally hit upon was a change in my agitation regime - not in terms of how long or often I was agitating, but rather how
vigorously. With every other developer I have used, a "standard" agitation involving fairly slow, gentle inversions has worked well (for what its worth, 30 seconds initially then 10 seconds every minute following, is what I had settled on). But for whatever reason, my caffenol-C developer seems to need very vigorous agitation to avoid the enhanced development on the edges. And when I say vigorous, I mean cocktail-shaker style agitation! At first I mixed up the shaking to include a combination of rapid inversions, axial movement, and rolling and twisting motions. However I settled on mostly simple (but very rapid) inversions - basically inverting the tank back and forth end over end as quickly as possible - and stopping to rotate the tank every few seconds so as to avoid having the air pocket in the same place. I still use the same durations and frequencies of agitation as before. I just shake a lot harder!
With this vigorous agitation the developer does seem to get quite frothy. Fortunately, it doesn't seem to have any deleterious effects however. I should add that I have settled on not completely filling the tank but rather leaving a bit of air at the top to enhance flow during agitation. Whether this matters or not in the present discussion I don't know, but I thought I would mention it in case anyone wants to try to duplicate my technique.
So I am looking forward to having someone else try this - someone who is experiencing the edge development problem, that is. Let me know if you find this helps, or if I am just hallucinating.
Oh and for what its worth, I have also found that adding 5ml (about 1tsp) of salt per 500ml of solution substantially reduces the fog in caffenol-C. I tried sea salt at first but I have found that common table salt (good ole' Morton's iodized salt) seems to work just as well.