Welcome to FT.
I would put all of the jewelry into a nondescript locked non metallic container and put into my nondescript carry on. When you place it on the belt wait until it goes into the X-ray before you go through the nudi scope or WTMD. By the time it goes through the X-ray you should be through too. If you can not find something that can be locked, just tape it up so it is sealed securely.
If you are traveling with another person have them go through the nudi scope first so they can be on the other side before you go through. Otherwise I would not be overly concerned with a private screening, death cert etc.
FWIW before traveling you might want to contact your insurance carrier. Many have limits on jewelry coverage (like $5K-$10K). As such, you might need a rider so that the full value is covered in case of theft (regardless if traveling or at a home).