I'm posting this to maybe bring some peace of mind to anyone else dealing with this.
I did online renewal, which I don't think is currently available. I completed the application in the evening of January 30th. Just now, March 14th, 6:45PM EDT, I got an email that it had shipped The email said to allow two weeks for shipping, but I'm guessing it will not take that long. Counting today, but not the date of application, 43 days passed. This was six days short of seven weeks. 5-7 weeks was the estimate at the time I applied. I did pay the $60 for expedited handling. I think I recall reading somewhere that they added two weeks to the estimate, citing staffing, computer problems, etc.
Other parts of this saga:
When I applied I answered truthfully about whether I had travel plans that included a departure date. At that time we had not yet purchased tickets, but did so soon after the application. I think I would fudge on this and pick a date of travel, if doing this over again. Our travel date is April 4th, so I was really nervous about getting it in time.
I found a phone number (855 865-7750) for technical support for the online process. I called on March 8th to see if they could amend the application to show our date of travel. After about 40 minutes on hold I spoke to someone who added the date. I don't know if that was the reason, but six days later it was shipped. He also said to call the main # if I hadn't gotten a message at the end of seven weeks. (877 487-2778 8AM-10PM, I think)
Before finding the tech # I tried this one a few dozen times over a 2-3 day period and never got through - only heard a message saying to call back at another time. Also, accessing the status part of the website only worked about 25% of the time.
The obvious message, don't delay!! Good luck to anyone waiting.