I have this problem often as well.
My best solution, albeit not great, is to find food that the jays don't care for too much, but the crows still value. For me, it's been puffy/baked Cheeto's. The jays will usually leave that alone, but the crows still mob it.
The jays are corvids too, so should be able to get the hang of the crow box. I have a couple that will throw the presented quarters in to open the box, but have never successfully gotten them to bring anything. And I am pretty sure of the group of jays, most of them wait for the "smart" ones to open it in order to get to the food basket.
Good luck!