I would only run it on a Laupa action. If you're stuck on that round, I'd look for a more suitable action. Since you want an improved version, I'd look all the way to a custom action like a Stiller, Defiance or something purposely built for the larger bolt heads. Weatherby MKV, actions would also be worth a look if you can find a cheap one.

If you want to use your 116 7mm action, a 7mmRUM would get you close performance wise. But you'd have to run those 195g's single shot. Next choice would be a 28 Nosler. I thing it gives the most performance that you gan get out of a standard length magnum action and still have a shot at it being a repeater.