Finally got a new battery from them. Seven weeks.
As related by the dealer, Specialized had three people each handling Turbo issues part-time, and with poor communication among them.
As a result of my incident and another of similar ilk, they are now said to have one person working full-time on Turbo issues, so the situation may improve.
I can't excuse them for this as it impacted me directly, but I'm glad the bike is operational again. However, I won't be buying Specialized stuff in the future.