The quick frame connectors do have their limitation. The first year we made our frame based on 8020 quick frame we had a similar problem. We used these connectors.
http://www.eztube.com/connectors/connectors.html
Note there are 2 versions. With a steel reinforcement and without. The problem with them is that they have 2 steps and the step near the joint is to big for quick frame. We set up about 6 students with files and mics and reduced them down. Gave the students something to do while the design was being finalized.
The steel reinforced ones are heavy but extremely strong. The composites may be good enough. The tower was supported by the bottom and top frame rails. We also have filled the voids in the quick frame connectors with epoxy putty and it did add some strength and stiffness. A very thin CA can wick in and bond a joint. 1/8 pop rivet can also help. Team 104 was limited by administration policy to hand tools and cordless drills. Quick frame was great under these restrictions.