Not being an expert I will throw in my opinion so the experts may point out the errors in my thoughts.
The key problem is the screws do not offer the strength you probably need (shear off or tear out)
I would infill the 2x6 with a 2x5 or 2x4 with the edge flush on top and receesed an inch or so on the bottom (fancies it up a little) and cut to act as a shoulder on the rafter end and jointed into the post. Epoxied together would stiffen and strengten it considerably, or bolt it in recessed holes and cap with 1 inch dowels.
Bob
