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Sounds like firm what you've said you've covered all the basics. There are sometimes some odd things that are overlooked or missed they can be small but can make a difference. When we get odd things like this there are several things we look for:
Tyres: though new we've seen tyres fresh off the tyre depots shelf with run out issues. On the ramp we have the car in the air standing behind each wheel looking directly at the tread pattern we get some one to spin each wheel clockwise then anti clockwise spending a bit of time looking at the inner, centre then outside sidewall.
The person says doing behind each wheel stays perfectly still as the tyres spinning they are looking for oscillation in the tyre tread block( noted as feathering) you'll see the tyre if it's out moving very slightly usually you'll see the smallest of dip either upwards and very occasionally downwards or even slightly sideways. It's a small movement but as speed increases so do the pressures and loads on the tyre and it's enough to create an issue though not oddly as we've discovered enough to bring an irregularity regarding balancing.
Common science would state that the pressures are always checked while doing anything in this area.
If we see something like this we'd also revolve the tyre putting our hand in the area of concern to feel the difference and again it can be very slight but it can be enough. If you're lucky enough to have the same tyres all round(difficult with a BMW these days) we would then usually swap wheels around and re drive to see or feel if the symptoms alter.
Doing what we do sounds like common sense but oddly enough when tyres are checked its a quick once over only that's done and not enough time spent looking at the obvious, as the symptoms come in at a certain speed chances are it's a rotational type problem. But I know these can cause grief and are frustratingly difficult to pin down.
Brakes: brakes gave been replaced, we've seen partially binding calliper(s)causing issues, often over looked when spinning the wheels around hence why we opt to look at brake efficiency using our MOT rollers, if you see the needle fluctuate on the rollers then Sod's law says when sped increases metal gets hotter and expands this will come into play more, you'll sometimes ex see this as a slight upwards shaking if the steering wheel, though again when we come across cars with this issue people on,y talk about the vibration side of things, rather than the steering wheel shake. But it's a long shot, but worth exploring as a calliper partially binding will create a shudder that some feel and find difficult to describe. We've seen countless disc pads replaced with a calliper issue in toe even though the calliper has wound back it turned out that when the brakes were changed some difficulty was encountered when performing the change.
Suspension: many times thus has been covered the arms should be an easy spot really obvious ones are the arms that everyone's been discussing in here usually from the drivers point if view I've discovered when these are on their way out you'll feel slight vagueness when driving when you tap the brake pedal you'll feel a slight judder, over speed humps at slow speed you might hear a slight squeak as the arms are loaded but I'd kinda doubt these are your offenders but stranger things have happened.
Others have wrapped up the rest re suspension
Drivetrain: your vibration could be traveling down the prop again the others have gone over this. One question I'd ask is after driving for a while when you select reverse after about 1-3 seconds do you hear a slight thud?
Hope this drivel helps best of luck finding the issue
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