I'm already on Tim's list for a "standard" CT12. What to do now? :-\
OK, seriously now. I believe Tim himself (but I can't speak for him) prefers the full air and detail of the original, although those likely varied, too. From what I recall (but again, don't take my word for it) Jim Jacobsen asks Tim to "tame" the capsules a little in the highs, for his (C12 inspired) Dutch microphone.
Still, such (a) large membrane(s) without the center screw will always sound somewhat scooped, albeit in a broad an smooth way.
You could try to compensate right at the beginning i.e. at the capsule, but there's only so much you can do there. Also, I'm not sure if that's a wise thing to do. More about this later.
You could also try to adjust the following circuit (for lifted midrange).
And you could try to compensate at the transformer's "end" (e.g. with one of the three T14 varieties Oliver offers).
Now, custom fine tuning for one's own particular needs can never be wrong and variety is the spice of life, but I believe there's a pitfall there, too. Leveling things to get it as close to flat as possible and make this a do-it-all microphone might kill the actual strengths. E.g. it will never have the mid attitude of a U47 anyway. So rather than trying to approach that, one could also embrace the broad scoop (with killer lows and true air band) and use it as a mike that will fold around others, adding width and depth to a mix.
Mmmm....... I'm maybe using too many words to get my point across. Just trying to start a discussion about this while we're still in the developing stage.
And why not invite both Tim and Oliver to join it.