Per https://github.com/discourse/discourse/commit/4382fb5facb035f5b414c6c7257dc828327a57c7, custom fields must now be added to a whitelist to allow editing by users. All that is needed is a single line in plugin.rb:
register_editable_user_custom_field :my_field
@gdpelican @LeoMcA I have updated the OP with this extra step, and also pulled in the comments from your second and third posts. Please feel free to update anything else you feel is necessary.