How tall are your walls, not counting the vaulted ceiling?
You do realize a 200" screen will nearly take up your entire wall?
200" diagonal 16:9 screen is 8'-2" tall and 14'-6" wide.
You would definitely need to go with an acoustically transparent screen in order to hide your front speakers/subs
( since you won't have any space available in front of a screen that size)
Most quality DILA/SXRD projectors would require a 20' throw distance (lens to screen)
to project an image that large, but you will have less than 17' left after you mount a projector and screen in front of your speakers
...which is a much more reasonable mounting distance ... throwing 20' to a 200" screen would require a VERY bright projector.
150" - 160" screen (6'-6" high x 11'-7" wide) would be a good match to a JVC RS500/ RS600 or Sony HW40ES/55ES with about a 16' mounting distance,
You may need a slightly higher 1.3+ gain screen though. That's a long throw and a large surface to light up.
160" screen at 14' viewing distance would give you a 45º viewing angle, well above THX recommendations of 36º
I sit 10' (eyes to screen) from a 120" screen (47º viewing angle) and couldn't take much more, well maybe 125"
If you think 160" or 150" screen is too small, just move your seating forward.
BTW....are you planning a single row of seating or adding a second row on a riser?