I believe you will need to replace the torque converter seal. (Possible but less likely it is the pump housing seal.) Your torque converter slides into the tranny, over the input shaft, and that seal is what keeps the transmission fluid from leaking past the case and torque converter as it spins.
The C6 is a tough transmission, many racers used them over the years due to their strength and reliability. Interesting is that the 88’ F250 2wd with the C6 had a higher tow rating than the stick version.
Be sure to measure how far your torque converter sits inside the bell housing. Torque converters can be a little tricky to get back in so that way you will know when it is all the way in. You have to twist them left and right and get all the components to fit in the torque converter. Like the Input shaft, pump, etc. It’s like putting in a distributor, you have to get it aligned with the cam and onto the oil pump shaft before it seats and goes all the way in. It’s not real hard but it may take a couple of attempts.
Be sure to grease or lube the seal so it does not burn up till it starts to naturally lube again. Here are a couple links you may want to look into. The first shows a C6 with the torque converter off. It is likely the center seal, less likely it is the pump housing that bolts to the inside of the bell housing. Second is some history on the C6.
BIG BLOCK 460 FORD C6 AUTOMATIC TRANSMISSION PACKAGE -- PASS36104
www.fordracingbyspeedshopdirect.com