Nobody arcs brake shoes anymore, well - not totally true.
The driver does after a couple hundred miles of driving and braking; the shoes will naturally wear into a compatible arc. I've driven manual drum brake classic cars for 50 years with zero issues and no "pre-arcing" in the last 20.. In fact, drum brakes saved my life in 2016.
Sounds like your mechanic isn't all that familiar with drum brakes. First off (as stated above) have your drums checked to make sure the material is still within spec. If the drums are in spec and not out-of-round then quality shoes are available at all
NAPA stores.
I've used their premium shoes and drums on dozens of classics with zero issues.
Next make ABSOLUTELY sure the shoes and springs are installed correctly. There are leading and trailing shoes and adjusters are NOT interchangeable side to side, most will have an L or R imprinted on them someplace. With good drums, quality shoes and a proper installation and adjustment NEITHER side should pull and neither side should have 75% of the shoe material NOT contacting the drums...
If one does pull its often deteriorated rubber brake lines that have "hour-glassed" internally, sometimes its a "stuck" wheel cylinder. Also cleanliness can NOT be overstated, any grease, etc. on the friction surfaces will cause poor braking on that side.
With the problem you are having I would get new shoes from a reputable supply house. Not finding someone to re-arch the shoe probably has less to do with asbestos and more to do with the fact front drums went out of fashion 50 years ago.
True!
Finally - the shoes have to "slide" on the backing plate, they are usually raised pads that serve as slide points. (refer to linked video)..if these surfaces get worn enough the shoe can't slide and the brakes can "hang up" (they also need to be lubricated during re-assembly). In such cases welding more material on the pads and grinding them back will fix the problem.
Notice in the video there is no discussion of "pre-arcing" the brakes: