The "L" bracket thingy isn't the problem although it would have to be added as you indicated. The stock material that blocks the detachable mag hole is the problem I was referring to. It would have to be removed.
Other than that, the demonstrated accuracy of the 12 FVs with the factory stock shows that it would be a reasonable choice even though there are some who claim it is too flexible.

I have an old 10 FP with a hidden mag and a solid stock that blocked the space that a detachable mag would use. The stock shot fine even though it didn't have the aluminum bed of the later Accu-stocks. I eventually replaced it with an adjustable Bell & Carlson because I discovered that the factory stock was just a bit too short for me. I think I still have the old stock, but it too would have to have the mag well space cut out to allow a detachable mag to be fitted.