Or is there another way to fix this problem.
Just something to think about. In a way you're trying to outsmart the OEM that probably has done lots of testing to see what works best. Not saying that is bad.
When I researched mine (different model) I found out that I should get what is called a "flow test" to see if cooler is OK. Flow test measurers how restricted or plugged up your cooler might be.
However...Ford wanted about $180.00 for test (I didn't know how to do the test) A new replacement cooler with me doing the work was only little bit more. So I just replaced original cooler. Didn't have to mess with new plumbing hoses or other stuff, just replaced cooler. Fixed my problems of running OK most of time but on long upgrades my temps used to get really high.
Haven't seen him post in awhile but a retired Ford trans engineer used to comment on here. If I could think of his name you could search his postings.
2003 Majestic 23P... Northwest travel machine
2013 Arctic Fox 25W... Wife "doll house" for longer snowbird trips
2001 "The Mighty Dodge"... tow vehicle for "doll house"