Enable, I agree there will need to be some adjustment considering that the rafters are existing. Still, I would use the approach mentioned above. Specifically, I would:
[ol 1]
[li]Try to get an accurate measurement of the roof pitch.[/li]
[li]Cut a test piece (something light) like a double 2x4 with the opposing slopes cut along the top.[/li]
[li]Check the test piece cut, and make minor adjustments as needed.[/li]
[li]Cut the actual ridge beam based on the adjusted cut of the test piece.[/li]
[li]Shim if necessary and/or jack up slightly (only slightly) to close any small gaps.[/li]
[li]Add blocking and uplift straps if necessary.[/li]
[/ol]
For me, this is how I would likely approach it. Cutting several birdsmouths seems like more work. The cut itself would be a pain. Cutting out the little triangle chunks would require either using an oscillating multi-tool or drilling a hole at the inside corner and removing the remainder with a jig-saw or similar all while up on a ladder. Assuming that the rafters are not true along the length (which they likely aren't), some of the birdsmouth cuts will need to be deeper than others as well for a tight fit, or shimming will be required.
I might also consider option 1 without shims if the loads are very light and crushing of the wood fibers at the sharp edge isn't a concern. Or if the loads are more moderate, I might consider the same except with a Simpson VPA connector or perhaps just an angle (L90 or similar) attached to the face of the beam along one leg and the face of the rafter along the other.