You want to cover the facia with thin material, esp since there is no need to build out the facia thickness. Therefore, you don't want to use the j channel there. Facia wrapping would be usually L shaped thin sheet. J channel is used for siding or such that has more thickness. Siding has a channel called finish channel which is about as thin as the siding material, but I wouldn't use this either since, assuming I understand your how-to, would be installed upside down and trap water.
If you don't want to make your own wrap with a sheetmetal and a brake, I guess you could combine corner angle to cover the facia bottom edge, then wrap with a flat sheet. Bring the sheet edge down past the angle which creates a drip edge. Once covered with gutter, you won't see much difference.
Hopefully you have a drip edge under the roofing. Top of the sheet would be held by the drip edge, and nail the bottom edge with a hole drilled somewhat larger than the nail. Also nail about 3' apart. You can also use a hidden clip to skip the nails and let the cover float. It is about an inch wide strip that's about an inch longer past the facia. When the sheet is placed, you bend the overhang over the edge. I don't know the name of it and can't find the image with whatever name I can think up.