My understanding of lenscast is that it is primarily a function of the angle at which light strikes the sensor. The more obtuse the angle, the more severe the cast. (This is a generalization. You will in fact notice bands of colour shift as you move towards the outer edge of the image circle. It is not a continuous shift).
Assuming this to be correct, then a centre filter should have no effect whatsoever on lenscast. It is designed to reduce illumination falloff.
The LCC function in C1 combines 2 algorithms - one to correct lenscast, neutralizing the colour shift, and the other to correct illumination falloff. There are sliders to control how completely you want to do this.
My own experience with shooting a LCC frame through the diffuser after each series of shots at a given shift would suggest that both colour cast and falloff are fully corrected even when using no centre filter. (Within a range of tolerance. When you start pushing local contrast as I do in most of my work, you will start to notice some small amounts of uncorrected cast).
The only circumstance I can see where using a centrefilter might help is if the level of falloff from centre to edge is so extreme that it is beyond the adjustment range of the software. The performance of this lens is not that bad, even at f8-f11 where I do most of my work.
As the process of using the LCC software is the same whether you use the centrefilter or not, I'm a little confused about your approach, Don. Am I missing something?
Perhaps Doug and Yair might like to share some wisdom?