Here is an exploded view of a scarf known as a timber frame bridle scarf.
I haven’t personally cut this one, but my program offers it as a type of scarf, so I thought I’d show you.
You should have your engineer decide on the peg placement. I just put in two to show possible locations.
I have encountered this bridle scarf joint in top wall plates in late victorian English barns, 2 examples opposite each other and within 18 inches of a supporting post have been displaced and split laterally, the age and worm eaten condition of the timbers may be partly to blame, but these joints have principally failed because of a failure of support under the posts and machine impacts on one post in the doorway.
I am currently righting the entire west gable end of this barn, one corner post and all the lower gable end wall timbers having rotted away and the bressemer spanning the gable end over the plates is rotted through. the entire end dropped 10 inches, many of the purlins are rotted through from rainwater ingress and failed lead valleys. I am having to form scarf joints for these repairs.
I was pleased to see many of the scarf joints I learnt from a reprinted 19th century book on timber structures reproduced on this site.
Thanks for your comment, would love to share any photos of this project on the site if you have any.