Ask the guys at Brownells if they know someone who could try this job.
The barrels you indicate are most likely too thin to safely reline. A more usual method, which has been done in the past if there's enough "meat" in the breech end, is to cut the old barrel off just ahead of the breech, drill the breech out, and then solder-in a new full-diameter, full-length rifled tube.
Even if the old barrels are badly pitted, it might still be best to give them a really thorough scrubbing and (non-abrasive) polishing, and than to fire only fully-jacketed bullets through them.
I have seen "slightly used" M.1903 barrels for sale on GunBroker.com. Magazines, too. The Remington parts may be harder to find, but you could try Numrich Arms. (Gun Parts Corp.).