That's a great idea, but unfortunately the Alpine stock fits the short action 1500 (243, 6.5 Creedmoor, 7mm/08, 308 size). Your closest option for the Mini is the Henderson stock like @
Dreamer recently got. I'm sure he won't mind posting up another pic!
I was thinking in a similar way recently, so got the short action 1500 in 223 as it comes with a hinged floor plate internal magazine that can easily be modified to take rounds up to 2.45" long. It also comes with 1:8 twist now as well. Dropped it in an Alpine stick which is a nice shape. It's shooting really well now and is light and trim with an 18.5" barrel and the same 35mm Gunworks suppressor you're considering.
The foreend on the Alpine is fairly short allowing quite a short barrel with the right suppressor if you decide to go down the road of a Creedmoor instead of the Grendel.