I would definitely still use the factory cooler in addition to the one you are adding. I run a 1996 CV in 24 hours of Lemons and Luckydog, we have a medium sized cooler plumbed inline with the factory cooler.

Our factory 4r70w got as hot as yours and wore out the 2nd and 3rd gear clutches. It did have atleast 168,000 miles but the heat killed it.