I wouldn't call myself an expert by any means....
However I am told that the box will go into a 'limp home' mode if its ECU goes bad or there is a dicky connection.
On mine I had an intermittent fault with the TPS for a while, and this also altered gearbox performance as I think it reads this signal. Basically the TPS signal needs to go low and stay low in order to allow the gearbox upshift in 'D'.
In 's' mode you won't get fourth gear at all, and upshifts are quite delayed. On mine 1st to 2nd is about the same, but 2nd to 3rd needs about 40mph. By contrast in 'e' mode it is in fourth gear by about 47mph on a light throttle.
Do double-check the oil level; this needs to be done with the engine running, otherwise the level will be wrong.
From your symptoms I might suspect a wiring fault of some kind. Maybe you have a ground fault on the kickdown switch wiring- that would certainly cause a 'no-upshift' condition.
Incidentally I looked at the ETK recently and there are at least four different version of the EH box that were fitted to the 6 series and I don't know for sure how many of them are comaptible either.
HTH
cheers