I have a Foxwell 520(?) Scanner. Where would I locate fuel trim testing? There is a Live data option with a number of choices. Hence my previous comment about the lack of details from their instruction manual or my inability to find the information.

An engine that misses at idle but runs fine at the high rpm indicates a low compression cylinder. You can gerrymander all you want with scanner and fuel trim but you have a low compression cylinder. Time to Break Out Another Thousands, wait that remark is for boat owners. LOL

Time to break out the compression tester.
Hopefully it works well down in those deep holes. Is there a special attachment that extends a normal tester hose?

Never had any problem with doing a compression test with my Snap on Compression tester. What type of compression tester are you using?

They look about the same. Mine are more generic I believe. So you get them hand tight and everything works from there? Everything I've tested in the past was much shallower.

Update..
Cylinder 1 ~158psi
Cylinder 2 ~158psi
Cylinder 3 ~158psi
Cylinder 4 ~110psi
Cylinder 5 ~110psi
Cylinder 6 ~158psi

Seems like the narrow space between 4 and 5 is compromised.
Is it worth doing a leak down test? Oh boy buy more tools.
No oil in coolant or coolant in the oil.
How much harder is a head gasket job on an m54 compared to an m20?
Is this time to do anything else at 165000 miles? Vanos seals?

Are you losing any coolant ? If so, You may want to swab cylinder 4 & 5. I recently had a stumble on start-up, a puff of smoke at start up, and I was losing a little coolant...very little

I put UV dye in my cooling system and checked for leaks in the usual places. Couldn't find any. I then pulled spark plugs and securely taped a q-tip (cut in half) to a foot long section of ethernet cable (flexible about 3/8" diameter). After the engine had cooled, I carefully swabbed each cylinder and sure enough, found coolant in cyl 6. Head gasket time.

If you don't have coolant in a cylinder, I might wager that you have a valve or two that is not sealing fully. Possibly due to carbon building up from a tired CCV passing oil into the combustion chamber, but that's just a guess. A leakdown might help narrow it down.

A head gasket on an M54 in an X5 (engine in car) is not too bad. I have done one before, and am planning another one this coming week when parts arrive. You don't need to put the car on jack stands and you have good access in engine bay. Use an engine hoist to remove/reinstall head and exhaust manifold together. I would also time-sert the engine block even if it never overheated. If you don't already have one, buy an under hood light bar for good illumination.

There is a lot more to a head gasket replacement, but there is a lot on-line on how to do it.

There is lot of debate on just replacing the engine in this situation. But in this E53 M54 situation, WITHOUT a lift, I think I prefer the in-car head gasket due to ease of access, and the hassle of engine replacement - dropping subframe with engine and replacing engine on front subframe.

Nailed another keyboard/Internet diagnosis.

Not worth doing a leak down test if you have low compression on two adjacent cylinders. The chance of having two bad valves in adjacent cylinders are probably a billion to one. You better off playing the Lottery and hoping that you win so you can buy a new SUV.

Acronym for BMW Break My Wallet.

So assuming I have all the tools I need, which I do have and experience tearing down motors completely and putting them back together except not an M54, what would the reason be to expect a dead motor rather than just a head gasket?
Any used M54 would probably need at least new oil rings from what I've surmised.

The fact that you have compression in both cylinders, and the fact that the engine misses only at idle but runs fine at high rpm I would just drive it and till it dies. It's a 19 year old SUV and the price has come down to the point that fixing the BMW will cost just as much as buying another BMW X5.