I've had good experiences of INN at all times of the year too but one diversion to MUC which ended up with a train journey to INN. Although it took quite a bit of time to do MUC-Munich Hbf and then train to INN I thoroughly enjoyed the train journey and the descent in to Innsbruck on the train was spectacular. By the time we go there INN had reopened and watching approaches and take offs from the train was pretty amazing.

If you have time on one of your journeys maybe make one of them to MUC instead and connect by train. I'd certainly do it again time permitting.