Thanks everyone for you helpful input!
miguelvp: That's pretty much what I was thinking of, I'm surprised that my google searches didn't turn any of those up.
edpalmer42: That's a really good point, I hadn't thought about the mechnical torque. I had considered the mezzanine board, but it results in two more pin headers and a pcb, which will add to the BOM costs, however I might end up going that way in the end.
Jeroen3 and Richard Crowley: Yeah, I know it's a pretty complicated solution, I'm tring to think of some good way to reduce the height, and your ideas help with that.
WarSim: Yeah, inverted headers with a mezzanine board might be the way I go.
Psi: What you found is exactly what I had found, u shaped headers, which are perfect for fastening something down, or using as clip-on test points, but not for connecting a ribbon cable from the under side.
mariush: Thanks for the lead, I was hoping to use a mid-cable connector, as opposed to an end, but searching for "low profile connectors" actually turned up some promising leads.
Thanks again everyone for your help. I've only just started wading into the pool, and your input has been invaluable. It sounds like the part I'm looking for doesn't exist becuase it just wouldn't be strong enough.