Внедорожный клуб "Вольные джиперы"

I've been going around in circles trying to decide where to take my Escalade. It's got a delayed engagement when I put it in drive first thing in the morning, takes a second or two before it actually moves. After that it's fine all day. I've asked three different shops and gotten three different answers ranging from "it's normal" to "your gearbox is dying." The dealer wants to strip it down and inspect which is a huge bill before they've even found anything. Someone sent me gearboxrepairsharjah.ae/brands/cadillac and said they've used them for a different car and were happy, but that's secondhand info and I don't want to gamble on this. Has anyone here actually used them for Cadillac transmission work, and did they diagnose properly rather than just guessing? I'd really rather not pay for an exploratory teardown if a proper scan can narrow it down first.