After trying the different possibilities, we think mapping works only for default JS files, and not for custom JS files.
To overwrite the JS we moved it to theme folder instead of overwriting it from Module.
The theme overwrite is working as expected.
Theme overwrite for `shipping-save-processor/default.js` is done as follows:
app/design/frontend/xxx/yyy/XYZ_AvaTax/web/js/model/shipping-save-processor/default.js