First, very nice looking X5. Unfortunate the trans is acting up. Second, your shop is great. Very upfront. Nobody knows these transmissions in any sort of "expert" fashion, with the exception of a handful, one being Phil as Overboost mentioned. He is amazing.
Funny, I am writing this at 3:30AM because I am replacing the transmission in our E70 (a variant of the same trans that is in your 4.8), also because of an E clutch fault (4F89 - 3/4 Gear Ratio Monitoring). It was determined through trial and error (only way to diagnose these without being one of the said experts). Had the valve body rebuilt with new solenoids, seals, etc. Tried fluid 4 times. No luck. Guys who rebuilt my valve body did warn me that it is likely an E clutch bushing/bearing failure before doing the work. Great service. So, end result, replacing our 166000 mile transmission with an 80000 mile unit. It is NOT a fun job, but that is mostly due to this truck being a diesel.
Anyway, if I were you, I would do (or have your shop do) a drain/flush with Valvoline Maxlife Multi Vehicle ATF. It's not recommended, and your shop will probably balk, but the fluid is MUCH thicker than the stuff spec'd by ZF/BMW for the transmission. If you are lucky, it will allow whatever in the trans is not building/holding pressure to do so again. It is a cheap attempt, especially compared to your other options and so you really don't have much to lose. $200-300 at a shop. The fluid itself is only about $50.
If that doesn't work, I'd continue down the path of least resistance. Full valve body rebuild with solenoids and Sonnax Zip Kit. Not just the solenoids. If that doesn't work... skip the rebuild and buy as low a mileage unit as you can find. Transfer your rebuilt valve body and mechatronics (TCU) to the replacement transmission. At least then, you will have a low-mileage refreshed trans. That's the exact course of action we took with our 6HP.
Good luck. Hoping to have ours back on the road in the next few weeks. Just got the new trans installed a half hour ago, but still have lots of other "while I'm in there" stuff and then of course putting all the diesel emissions stuff back in the truck. Think 10lbs of "stuff" in a 5lb sack.
Here is a great source of information for ZF transmissions and specifically the 6hp.
https://axleaddict.com/auto-repair/Z...E-Clutch-Fault