OP,
Having never seen or used a control strip, I have a few questions related to what you've said :
How could a blank film have any CI or G-bar or gamma other than 0 ? Or do you mean something other than unexposed film when you refer to "blank film"? You later say "...then all TMY developed for 8 minutes in DK-50 1:1 will be developed for a CI of 0.56." OK, granted. However, I don't see how an unexposed TMY sample could be developed to a CI of .56 even though it may have been developed for a CI of .56.
Aren't these control strips exposed to the same value? I'm assuming they are samples of film stock (e.g., TMY) exposed to a calibrated exposure (e.g., exposed to some standard lux value through a calibrated step wedge). Is that what you mean by "calibrated test strip"?
I take it you refer to different yet equivalent combinations of film developer dilution, time, agitation, and temperature when you cite the "degree of development." IOW, one could achieve the same "degree of development" with the same control strip developed at Time A + Temperature B or Time B and Temperature A, OTBE. Such an equivolence in development would lead to identical CI values.
Joe