IMO, do not overfill it at any time.
Did you drain the convertor or did you just drop the pan?
C-6's usually have a removable plug on the convertor, which can be accessed through the back side of the flex-plate.
As far as plumbing you trans cooler:
Automatic transmission cooler guide and installation
Transmission Cooler Quick Guide & installation
The most often asked question is should I bypass the radiator cooler when I install a auxillary cooler.
Most cooler manufactures and automobile manufactures information we have read, recommends installing the coolers In-Series with the factory radiator cooler for maxium cooling efficiency.
So unless the manufactures who have spent 1000's of hours testing different installations are wrong, the suggested cooler installation is in-series......
Transmission > Radiator cooler > Auxillary cooler > then Back to the transmission.
If you must bypass the radiator because the cooler tube is leaking or for other reasons, be sure to increase the size cooler you install by 1 to 2 sizes.
When I worked for Ford, I recall a TSB advising that dealers should always install an "H-Fitting" in the line if the vehicle was equipped with a tranny cooler, particulary in cold-climate regions like ours.
This fitting was designed so that the tranny would not be starved for oil due to cold-temperature oil viscosity. Tru-Cool brand coolers have a similar technology built right into their "LPD" series.