No delay and no announced schedule.
Your source at the Museum didn't offer any useful info.
I will be very surprised if General Motors truly has no planned point-in-time for start of regular production.
From a PR standpoint GM is wise not to announce the planned start-of-production. With a car which is as new as is C7 (think the change-over from C4 to C5) there are bound to be some problems and a wise management would have allowed some extra time to "work out the bugs".
Customer wants, marketing beliefs, performance goals set by engineering and government regulation have driven the addition of a lot of highly-technical systems on that car. Getting them all to work properly and in synergy in the real world may not be easy. My intel from some good sources but not confirmed by second sources tells me there might be some significant challenges the Corvette Team is working on very hard to meet. If that's true, it may take time to meet those challenges.
We're in the last week of July. I would guess that BG is going to have to start building cars for sale fairly soon if dealers are to begin deliveries at the traditional start of the model year.
I tend to put more faith in Rob's opening post than one by a screen name who's only posted one time to the CAC and quotes an unnamed source at the NCM. Also, that Rob has never retracted his statement and official GM remains silent on this issue speaks volumes.
Not being on the media A- or B-list, I'll not get an invite to the media preview for the car, but if invitations to the 2014 Corvette Stingray "long-lead" media event have gone out to A-listers, that's a good sign.