This turned out to be a conflict with the SqueezeWP plugin. That plugin adds an admin menu page at a preset position which overrides the Testimonials menu.
According to the Codex, there is a way to reduce the conflict but there does not seem to be a way to truly prevent it using the standard WordPress methods.
It seems like a weakness in WordPress because the method I use to add a menu page, as part of creating a custom post type, simply accepts the next open slot so there’s no possibility of overriding another menu. The method used by SqueezeWP forces a specific position. I wonder how many other “near misses” are out there?
So I modified their version of Strong Testimonials to accomodate SqueezeWP. I will build a proper solution into the next update.