Thank you very much for giving my idea a try!
Your data does seem very sensible, and I would trust it. Your choice to measure the light as a mule actually circumvents the main weakness of my idea, which is noise sensitivity of the 1/cos^4 term: even a small error in angle measurement can blow up in the 4th power. The cosine function is most stable at angle 0, which is where you performed the measurement!
For lights that cannot be made into a mule, I proposed a (hopefully more reliable method) for integration in another thread; the idea is to use a sheet of paper to diffuse any beam into a Lambertian profile, with the scaling/calibration constant determined by measuring a light with known output. Experimentation suggests that it is much more reliable than the integrating shoebox, which is great considering how much easier it is to build.