[wCYvMKAc]

Thanks for your input. Kote-men now feels like a rip-off: Get the kote without the men and no ippon (I have enough difficulty getting either one by themselves let alone both in succession...). Your answers also confirmed my suspicions.
If I understand this properly the point of kote-men really seems to be to get the men (the kote being somewhat "optional" since the men will be given regardless of whether or not there was ippon on kote): i.e. If you want to get kote just do kote.
And yes, I also use the kote as a "feint" to get men-uchi. Works pretty well sometimes....and other times I just trip over my hakama.