I can't get a good sense of your camera's type of movement from the shot you provided. If the camera isn't changing its
position (only panning and tilting, essentially), then you only need one or two solidly tracked points to get the job done. Note that this is sometimes possible with handheld shots, if the camera remains in the same physical location, more or less (there may be some drifting when trying to "solve" a handheld shot as a camera-on-a-tripod shot, but with some shots it's the only possible solution).
If your camera is moving through physical space, then you're probably going to have to reshoot. For one thing, your tracker points are all on the same plane -- you need
depth (foreground objects, background objects) in order to get a good 3D solution. And your trackers need to be spread out on the back wall. (You probably already know all this, but it's worth pointing out for other people who might stumble across this post.) The only possible thing that could save this is the rigging and other trackable data at the top and sides of the greenscreen (we only see it briefly in the shot you provide). If you have footage that includes those elements you might be able to grip onto something. But frankly, in my opinion, things look bleak if your camera wasn't on a tripod.
Ben Unguren
Motion Graphics & Editing
http://www.mostlydocumentary.com