Solid advice so far. I would add that a cordless impact and deck screws will probably work great for this, unless your existing rafters are really rock hard. This can certainly be the case with some species that are dense and had the chance to dry for most of a century. In that case, you may end up actually breaking a lot of screws off. The other option would be an air powered mini palm nailer. I have a cheap one ($39) that works awesome in cases like this.
The other issue is one that any framer will tell you can be a challenge. The new tails, and facia will be as straight and crisp as the top of the existing wall is. In new construction, any competent framer takes great care in the "line and plumb" process of straightening the walls, prior to installing rafters. This involves using a string line, or laser line, and pushing, pulling, and bracing the walls to get the outer edge of the top plate deal straight. After that, well cut rafters will slam tight to it, and the facia will be dead nuts beautiful.
In your proposal, if you cut every false tail exactly the same, with the exact birds mouth, you will follow the existing building exactly. It the wall is wavy, your new work will really show that. I would do one of two options. I would cut and nail the tails at each end then stretch a string from one to the other, to measure each added tail. OR, I would reduce the dimensions of the new tail so that the board was narrow enough that it didn't need a birds mouth. Then you could just have a plumb cut on the end, and slide the tail up and down the rafter, till it met the string line. I have do this before, and it's quick and easy. Precut all the plumb cuts on a chop saw, hold the tail flush with the top of the existing rafter. Slide down until you just about touch the string line and shoot it fast.
Hopefully. I have explained this somewhat clearly? Good luck.