while it's generally recommended to have as simple a signal chain as possible,
before plug-ins, back "in the day" it was quite common to use EQ, comp, (and sometimes reverb or a tape loop) on tracks on the input signal chain
I still use EQ, or compression on the signal chain if I'm familiar with the artist and the gear being used. I have a pair of old Altec 31 band active EQ's that I slap in the chain.
For myself, I'm stronger at ~ 1.25K so I'll cut slightly, but at ~800 I'm a bit weak, so I'll boost there, and because the tube mic picks up a lot of "room" I'll cut everything below 160- If I'm using the A-T E3300, I'll use the lo freq roll-off built into the mic instead of the EQ cuts down low
I have a female singer who just blurts out really noticeably ~2.5K on the ribbon mic
another friend who's nasally and sounds especially thin above 3K, so he gets a boost regardless of what mic I use on him
In all three cases the same set-up with person is used and the adjustments seems to eliminate the distractions (each of us is aware of where the trouble freqs are for us)
as to the C1, is it just your voice that the mids sound harsh in, or most any use with the mic.? I've not seen a curve for that mic, but perhaps there is a boost inherent to the mic at those ranges...
OR it could be placement in the room (reflections/standing waves)
or- for that matter could be an artifact of the pre-amp
and there's always using a splitter and taking a dry track- signal level may diminish slightly but may not be enough to warrant concern beyond boosting the gain slightly