The main considerations with replacement vs restoration, are whether you have asbestos or modern composite linings, bonded or riveted linings.
Drum brakes were never intended to run anything but asbestos linings. When the great switchover occurred in the trucking industry, there were exploding brake drum stories nearly every week. The non-asbestos linings get hotter, and require significantly more pressure to achieve the same level of braking as asbestos linings.
So, if you have asbestos, consider saving them. If you have composite linings, throwing them away is a viable and desirable solution. Don't mix lining types!
Riveted, or screwed brake linings are the mainstay of heavy truck drum brake systems. Bonded linings are standard on car drum brakes. Oils and fluid contamination can sometimes (rarely) damage the bonding substance (glue isn't really the right word) used to fasten the linings on bonded brakes. Riveted linings don't care, as they are mechanically fastened to the shoes. Deuces should all have riveted linings... I don't know if bonded linings ever show up on deuces.
That said, I have restored saturated linings numerous times. For oil soaked linings, it takes a sequence of scrubbing down with brake cleaner, and heating the shoes... Just like with oilite bearings, heat forces the oil out of the lining material.... Heat them on a pad of newspaper, and after they stop oozing, wipe them down hot with a cotton rag. When they cool down to just warm scrub them with brake cleaner again. It shouldn't take more than 1/2 hour. Brake fluid soaked linings are comparatively easy. With highly water soluble DOT3 fluid, a simple sudsy water wash down is all you need... Simple Green works well. With silicone DOT5, a brake cleaner scrub down will do the job.
One other thing: Passenger cars with drum brakes usually have servo brakes, meaning that the brake shoes are free to pivot in such a way that they self actuate, making pedal pressure lower. If you clean linings with servo brakes, and the linings retain some of the contamination, they can get grabby as the vehicle slows down. This can cause the contaminated brake to lock up hard, making control of the vehicle challenging. The moral is do an extra especially good job of cleaning the linings on servo brakes, or more simply, just replace them.
The Deuce does not have servo brakes. It relies on a very powerful air assist system to make the pedal pressure acceptable. The brakes won't usually lock up unless something is severely worn out (drums, shoes), or broken.
-Chuck