The first thought that came to mind for me is Electra makes these. Here is the link: Electra Linear Cup Holder

Electra, traditionally made good stuff. I see that this is $25 and that is without shipping.

You could probably check this out in person and hold it and see if your favorite cup fits in there if you have an Electra dealer nearby. What about the bike shop that sold you the Jamis's? I've seen them in Walmart, but their availability is probably in the spring time when they load up on their bike accessories. Otherwise, you can check out other bike shops near you.

The reason I'm advocating for in person is that this is a bit like shoe shopping. You really need to see it and see if your cup will fit and will be able to be inserted and removed easily while staying in place while you ride.