You may not need permits for a repair in your area. Most places do not require them for an "in kind" repair. They may or may not want one for the coverage. the permit remark was for the benefit of all who read the post for a host of projects. If you have a permit, you have someone who is supposed to look out for your best interest!
Now, at 10', this is not a big job. Depending on the width of your overhangs, and the grade near the barn.
Did you have soffits before? If not, I would not install wood just to go over it.
To expand on what I said before, using F channel with a nailer above it, (2 X 4), against the barn and using a piece of strapping attached to the bottom of the end of the rafters, you can nail the soffit panels on each end and keep locking them together until you get to the end.
Your new fascia boards will be cut to run 1/2" below the strapping so as to cover the ends of the soffit panels. And then the aluminum fascia will have an L bend of about 1 1/2" to cover the soffit panel below.
I don't know if what you have is as easy as that but, it can't be that bad!
Again, Good luck, Jason
Ps. I do not want to re-invent your job, I just think this would be the way to get the most ventalation!