Welcome 8ball. Are you talking about bracing from top plate to post? I have to admit those are some big braces. Are you going to put an arc on the underside of the brace and how much from the edge will the center point of the arc be laid out. I did a quick draft at 2.5" and it looked alright.

Since you are dealing with compression joinery it gives you more flexibility than say a tie-beam to post joint. The brace joinery is in compression as long as there is a mirror equal in the same plane somewhere. In my opinion since there is no tension on the joint I would use a 1 1/2" wide tenon so more of the post wood is left. I do not know if you are centering these braces and mortises. However even if you go say 2" from a reference face, then a 1 1/2" mortise you still have 4" of wood on the other side. I would think centering the mortises on the post would be best. If you are square ruling just say 3" from reference face. I would think that offsetting the tenons is unecessary and might be worse for post strength (anyone?). I would put the mortises in the same place on each side. Under normal brace dimensions (3X5) I would also just make the mortise a thru mortise for both tenons and be done with it.

The 5x8 (assuming no nosing on the brace and it is 12/12) will require you to cut 11 5/8" of mortise in the vertical plane of the post. I still think this would be alright as long as the tenon is 1 1/2". I could be terribly wrong on this particular instance though.

Also with a 3" tenon a 3/4" diameter peg would be better according to some rules I saw somewhere along the way (3/4" dia for tenons less than or equal to 4" in length).

It would help to see the frame as a whole.

mo