the whole barrel will be kept in inventory with future fixes in mind.
The first airline to experience a tail strike will be more than happy to buy the lower portion of that barrel...
Cut out a few test pieces from the burnt section. Test them to see how much strength was lost (and I expect it would really not be that much).
You are again metal minded (nothing bad, that´s what 99% of the aviation people are). If you "cut out" a test piece it will fail where you clamp it into your text fixture. Composite test pieces must be especially designed and build to really load them realistically and get test results you can work with. Coupon testing of composites just makes sense for certain specific properties, otherwise you should test larger pieces of substructure.
Replace the whole barrel in the factory.
That would require a design of the joints to allow for re-drilling and using oversized fasteners. I am not sure whether Boeing has designed the barrels for that. The fact that they had to remove the window at the joint seems to indicate that it is just barely possible to do the joint with no strength penalty. Re-doing the joint by re-drilling the holes may not be possible. Just like you can not do a simple rivet joined in the pocketed area of a chemically milled fuselage skin, the composite layup needs to have higher wallthickness and different layup for bearing strength in the area where you want to install fasteners. Unless you build your aircraft from "black metal" and waste a lot of weight on panels which are strengthened for fasteners everywhere. As we did in the past, just to allow riveted patch repair everywhere.
If Boeing is doing the composite repair right, using the same technique that is used in small composite aircraft since 1956, and regularly inspects this repair during the remaining life of that aircraft to collect data, potentially doing a destructive test of that repair once the aircraft retires, then this incident and the according repair may mean a quantum leap in large aircraft composite design. It would mean we finally build and repair large composite aircraft, not large aircraft from "black aluminium" anymore. This could be the long term test that should have been done 20 years ago to get confident in real composite repair.
In 20 years we will laugh about riveted titanium patch repair of composite aircraft, just like the small aircraft industry is laughing about what "the big guys" do up to now.
And maybe some day we will even learn that there are more clever ways to build composite aircraft than using stringer stiffened shells and ribs/frames with mouseholes cut into them joined by clips, cleats and fasteners...