You have the scarf idea, however you will need to extend farther in order to give more wood behind the peg. 6 x 6 should work for posts. I am concerned over the beams capacity.

Two options if you cannot obtain larger timber.

1. Shorten the span by adding another post.
2. Assemble built up beams from 2 x 10 lumber.

Consult local building code for loading standards, then design the structure.