As far as I know, Sims only offer bespoke; and machine-stitiching is not a bad thing - do not confuse bespoke with hand stitching
Keep the process simple, do not source your own tweed. Both will have access to a lot of tweed cloths, unless you want something unique.
You need to decide if you want to pay £800 more for hand-stitching. From your post, it seems you should go with Sims; however, it would be helpful to know your suit experience.
My only experience with Barkers is a pair of Arnold purchased six years ago. The sole did last longer then I expected; however, not worth resoling.
If on a tight budget or starting out, they are worth considering; however, I would rather spend a bit more on Cheaney.
There a few threads on Moonbeam, if you use the search function. Why Moonbeam for a suit, more suitable for sport jackets
Agree with ET that about your first bespoke suit; add charcoal grey to the list as well, although I think mid-grey is the best option
As for M&M, did you discuss your prefered style with them or did they recommend Fred after having a general chat.
Why not get it made bespoke from other tailors. Cad & dandy, graham brown, or one of the tailors on and around lamb conduit street. You get bespoke but no sr bespoke
In this way, you can get a fitting as well