We are in a similar situation- trying to get a driving record for my husband from the cantonal car transport department (DMV-equivalent) to submit to US auto insurers.
We are based in Zürich, so here is the relevant link for this canton:
http://www.stva.zh.ch/internet/siche...Mregister.html. If you Google "ADMAS" and your canton's car transport department, you should find the relevant webpage for you.
Per the website, we sent a letter to the authorities asking for his excerpt from the federal ADMAS register, including a copy of his Swiss drivers license. Unfortunately, we experienced a hiccup with this, as he wasn't found in the register, so we are trying to find another approach. However, this could be an exception, so this might be worth a shot for you.
We did not own a car, but were Mobility members. Thinking out loud here, I wonder if Mobility could provide a driving record. To the OP- thanks for inspiring this line of thought!
When we successfully get a copy of his driving record, I'll post an update.
Good luck!