Just a bit of follow-up. I ended up sending the OTA to Celestron. They confirmed that the mirror was not attached to the supports, and removed the old RTV, re-attached the mirror with new RTV, rotated the optical components to get the best alignment, and collimated it. With the mirror removed, they cleaned and re-greased the slider, and cleaned all the optics. The cost was the same as the basic service. The shipping was actually more expensive than the service. The scope is on its way back, and I'll post new shift numbers once I have time and weather that allows me to check it.
The repair experience was a bit mixed. On the one hand, I got to speak to the repair supervisor who was extremely helpful and knowledgable. But the email communication was a bit confused. I emailed a description of the problem and a list of other things I wanted checked. When it arrived, they sent me email saying that they would clean and collimate it and return it. After a few emails, I finally got to speak to the supervisor who said he would ensure that all of the issues would be addressed. After a couple of weeks, I got another email saying that my OTA had been cleaned, collimated, and was being shipped. So once again I called to be sure that they actually did what I asked. The receptionist couldn't reach the repair supervisor, so she scrambled to get my message to the repair department and called the shipment back from Fedex. The supervisor called me back a couple of hours later to assure me that it had been serviced as requested, and that they had confused it with another OTA in the email. Now they are shipping it again. Basically, when I was able to speak directly to real people, they were incredibly helpful and responsive. There just seems to be an issue with connecting email for service requests under ticket numbers with email related to receiving and shipping.
But, to partly answer the original question I posted, the amount of shift I was seeing was indicative of a serious problem in the optics, and was outside of the norm. I have to wonder how long it has been this way. The previous owner was complaining that his mount was not working and needed to go in for service, but that could have been due to the impossibility of building a model with inconsistent star positions. It also makes me wonder how many of the people who have "fixed" their shift problems by tightening the retaining ring are actually dealing with separation of the RTV on one or more arms.
Just as I suspected and wrote in post number 42.
The good news is that after my C11 came back from Celestron, collimation (with normal handling) held really well. And I had no additional “mirror flop” issues for the remainder of the 13 years that I owned the scope.