Well, Alps responded to my email, but the answer was as expected:
thanks for your interest in our products.
However, we are not selling any spare parts to end customers.
Please contact the producer of your device and ask for a spare part.
Also for us it's very difficult to identify which part you exactly need.
Bose is selling spare parts, but only on "component" level. This thing is around 70-ish USD + shipping. Didn't found refurbishing kits of any kind for this particular model.
nctnico, I didn't checked the topology, so I can't say if the audio is routed trough pot or not. I can only say it is not hi end product, it's just elegant and expensive.
I'll leave it now as is, until my friend start complaining about scratchy pot again.
You need to watch out whether it's linear or log as well. Other than that I don't see why a 3/4 turn (of same value) wont do the job if you bodge it in mechanically with flying leads. Sure it won't match the legend but always better to make your own new legend/scale numbered 0-11 in any case.
It is log pot (see drawing). 3/4 turn pot will work only if the first 1/4 turn has the same curve as the existing one, because the wise designer @Bose made the volume wheel mechanically stop after 1/4 turn. There is no scale on it, it's left to the users ear.