I have a Rex Merrill “silhouette pistol” in 7 mm Laser Jr, purchased from a local dealer.
It came with cases formed from .307 Winchester brass shortened to 1.595” and a set of dies.

I can find no load data for it anywhere and am hoping someone in your organization has some.

I have not personally worked with this case but it sounds just a little bigger than a 7 BR case.
I would think a mid-range 7BR load would at least give you a starting point.

I hope this very late reply will do some good. I also own a 7mm laxer jr. I have cases,dies and if dig deep enough I can come up with loading data. I hope this helps someone