You're right about the test kits. If the USD becomes worthless and metals become common currency we'll all have our own test kits. Most silver testing uses the same acid as in this $5.50 kit from Amazon. It won't tell you the exact purity, but you can be confident it's "mostly" silver and I can't imaging there being a problem of people casting rounds and bars from 70% silver.
Drill a hole with a small drill bit and test the chips from deep inside.
Volumetric testing for density is easy and should catch most fakes