Thanks all for the confirmation that there are no flaws in my equipment, and that the incompatibility is a design "feature".
Since I was not specicifically planning on stacking extenders, I don't think I will need to swap to a 3rd party 1.4x, but it is good to know that there are many good options.
Gasrocks, I'm not sure how combining equipment already in one's bag to experiment counts as trying to "beat the system" and makes the user "power hungry". I didn't buy the 2x specifically so I could have a 560mm f/8 (stacked with my 1.4x) I bought it for an autofocusing 140-400 f/5.6 with IS, which by most accounts can produce acceptable images at much less cost and weight than buying a 100-400 and carrying that along with my 70-200. Stacking teleconverters was only an experiment (partially to look at focal length differences) since I am considering a 500/4 for an upcoming trip. I'm fully aware that the IQ from stacked TCs would be marginal at best, and not comparable to the native IQ of a long prime, but I was interested in experimenting. (And it looks like you own 4 teleconverters yourself, so I see that you can recognize at least some value in the tc concept.)
I guess I was not doomed to failure because of trying to stack extenders, but in trying to stack CANON extenders. No biggie. 
Thanks again, everyone.