Just a few remarks:
I use both the traditional and the New cyanotype process.
Traditional cyanotypes do need considerably longer exposures than Mike Ware's New Cyanotype process. This process also tends to give deeper, nearly black blues, and a longer tonal scale, much like a platinum print. It is also possible, as far as I can see, to control contrast much more efficiently with this process. It is, however, very sensitive regarding the paper base.
It goes a long way to pre-coat a paper with a citric acid solution to enhance the quality particularly of New, but also traditional cyanotypes. Don't use oxalic, and don't use Vit.C - it's not the same as citric acid.
Traditional cyanotype is spread much more easily with Tween 20 - better than photoflow. It may also be used for New C. depending on the paper base.
Regarding this COT-something paper, I never tried it and I have no intention to do so (I don't like the Bergger company as they have intentionally spread false statements about their manufacture of films), but if it's really got an alkaline buffer it should not be marketed as a printing paper for alternative processes.
For traditional cyanotypes, the quality (acidity) of the first wash water is of critical importance.