As far as I'm aware I never developed oedema.
Before I started running with Vibrams for a few years I played a lot of pickup sports on grass fields and almost always played barefoot. I always noticed how sore my feet were the next day (obviously the more I did it the less sore I was) bc I was using muscles shoes don't let you use. Once I started running with Vibrams I ran almost entirely on trails (sometimes tracks or fields) because running on concrete gives me shin splints and is very uncomfortable for me - regardless of shoe.
I've never run a marathon and the most I've run in one go was 8 miles. Straight jogging isn't, from what I have read, good for you. Walking and sprinting are, however. So these days (maybe 10 years after starting to use Vibrams (and I'm 29 yrs old)) I often will run walk and spring occasionally, just like athletes do in soccer and ultimate frisbee, on trails. I like wearing Vibrams bc I like feeling the trail - although occasionally that results in stepping on a sharp rock (I wear the very minimalist style of Vibram). I definitely land on the balls of the my feet more and I think my running is better with them on compared to shoes. I'm more aware of my movement and the trail.
Running is a high impact activity, so idk about how to continue it w/out unacceptable pain unless you run on very soft surfaces? Maybe you could mix in sprints and walking on a grass field? Also exercises on grass that cause you to move laterally to build up your resistor muscles. Then maybe after doing that for a while you could transition to running in Vibrams or another minimalist shoe.
Have you ever tried swimming or rock climbing? Both are incredible exercises that are low impact and great for you. Rock climbing develops all sorts of esoteric muscles and it's fun too.