If you can find someone to RELINE that Gibbs to .303, that would be the simplest way to restore it to an appropriate chambering. PacNor barrels (in WA, OR????) used to make .303 barrels. If they still do, a skilled gunsmith could use one of their blanks to make a liner, assuming there is enough "meat" on the remaining Gibbs barrel to allow a thick enough liner to be fitted. That would have the merit of allowing you to use the original forearm, and simply find appropriate sights to replace the ones originally on the rifle (probably not a simple thing to do, but not impossible, either).

This job would require a gunsmith with sufficient cojones and confidence to do a liner for a relatively high pressure ctg. (some won't) and who will take the trouble to find or rent a .303 reamer (no common but available). Possibly someone on this forum knows such a hero. I would like to know who would do the work, since I have a beat Ruger 1A 7x57 with a 16 1/2" barrel (Thanks, Bubba!) that is aching for a 28" .303 barrel (probably not a reline, tho).

The next easiest thing to do would be a reline to .32-40--seveal guys can/will do that. And the chambering is not unknown in British rifles, although I don't know about Gibbs.

Good luck and let us know how the project proceeds; I envy you the opportunity to restore your Field!