It seems that TCS requires your vehicle to Swiss-registered. Their reciprocal agreement with AAA looks to be quite sparse and may or may not include a discount for breakdown assistance.

Any other options?

We used TCS for our UK registered car when we broke down on the swiss french border, and they allowed us to join and register with them knowing our car wasn't swiss registered, so they can do it. Our car is now swiss registered and I just changed the number plate details on their website.

Give them a call and see what they'll do.