Depends on the car, but generally I start with parts stores and see what's available.
If I was in your shoes, and I have been, I pull the drums spray down the dust and assess everything first.
I only replace drums and disks if there's not enough thickness to have trued up. It took a little looking (calling) but I found an automotive machine shop about 40 minutes away that still does that.
Backing plates had grooves, so I've have had to weld and braze those and then grind down. On thronts it won't be so bad to remove and do those if needed. On the rear, the axle halfs have to be removed. I've tried doing them with the axles in. Doesn't come out as well if the weld build up is too high because there's nothing to reference when grinding and filing down.
On second thought, based on the description of your problem, I might start by bleeding the brakes. Once the drum is off that can't been done. So that's where I would start after maybe a quick visual check with the drum off and everything washed down. Then reinstall the drum and bleed.
