Since the low speed is working normally, the effect you describe - -
"The issue seems to arise when it hits heavy traffic after a fast drive on a motorway or similar."
- - sounds to me like a heat soak effect, as alluded to by
Kaiser.
There's a simple way to check this. Repeat the routine so the 'high' speed operates after a brisk run. As soon as it's safe to do so (within say 5 minutes) park up and turn the engine off. If the fan continues to run (for up to 10 minutes from the point 'high' speed came on, then it's heat soak and a normal function of the system. You can see this in the operating parameters of the older 3-speed system. Unfortunately, MGR never got to produce a similar diagram for their later 2-speed models, but a similar function will be retained. However, if the fan stops when you turn off the ignition, there's probably another factor to look for.
When replacing the original 3-speed system with a plug'n'play 2-speed, you obviously drop one of the old settings. I can't remember which one, but it doesn't really matter. You only have two speeds.
Of course, the heat soak events may be more frequent and from less obvious situations if there's an underlying cooling system/coolant problem.
TC