Been there done that!
I had all the same steering slop in my GMC SLT 2500HD, F! 6000ish miles
I took it to my local GM dealer along with PIT 5501C.
They read that 5501C and started to laugh, literally.
They confirmed the problem/fluid leak and ordered a complete new steering gear box( which was on national back order and took a week to arrive), they didn't even try to follow protocol in PIT5501C.
Today I took the new PIT5501D into the dealer and talked to the mechanic that worked on my truck, I guy I trust.
He told me, he would never try PIT5501C or D. . He told me it is a very complicated system and setting it to OEM is difficult and that I would never be happy with the steering if they attempted to follow the PIT5501 C&D. That's why they just ordered a complete new steering gear box to begin with.
Fingers crossed all good now.