The link you posted shows that there is a configuration that a guy is using, but Yakima does not recommend that for an Edge. I think I know the reason why. I had a 1999 Volvo with no cross bars. The official solution (Thule and Volvo) was a rack that clipped into the door frame similar to what the EdgeForum guy suggested.
Here is the difference. The Volvo door frame had a dimple in the sheet metal where the rack attached on the door. This dimple served two purposes. First, it showed you where to put the rack, as there was additional support for the weight of the box under the sheet metal of the roof. Second, when the rack was clamped down properly, the dimple was enough to hold the rack in place in the event of a sudden braking or forward collision.
I'm not saying that you shouldn't do what the guy in the FordEdge forum did, but I want to point out a couple of dangers that he didn't mention.
In the event of a frontal impact, your cargo box will continue moving at speed. There is nothing but friction to hold the rack to the car. I have seen kayaks on a rack go sliding forward, off the car, rack and all, and into oncoming traffic because the rack was not tightened enough on the flush cross bars. Maybe the length of the window frame on the Edge is enough. I don't know.
I don't know the laws in your state, but if you do not secure a load properly in New York, "...a motorist who fails to secure his or her load can be charged with a misdemeanor, a criminal offense, and be even given up to 30 days in jail. Further, that motorist can be personally sued if he or she negligently secured their load and it causes death or serious injury..." This was the ruling of case of a person who didn't secure a mattress on top of their car. Who knew? Also, on some insurance policies, your insurance can be void if you are in violation.
Finally, the saying, "A chain is only as strong as it's weakest link" applies here. Yes, the roof may support 100# (and I believe that there is an engineering tolerance built in anyway), but where? On the sheet metal or on the frame or on the plastic cargo bars? How much does your box weigh? Mine is 42 pounds. Add the rack and crossbars and mounts? You aren't going to be able to put suitcases up there. Skis, poles, coats - sure.
I like that you are doing all the research. You will find the right car eventually.