I’m not seeing anything in the plugin that would cause the user fields created through it to be removed from the database when the plugin is removed from a site. What I’d expect to find is that from the Rails console, running:
UserField.where(field_type: 'multiselect-dropdown')
will return the list of multiselect-dropdown fields you have created on your site.
The values set for the id of each of those fields can be used to find the options that each user on your site has selected for the field. For example, if the ids that are returned are [1, 2, 3], there will be corresponding UserCustomField entries with the names "user_field_1", "user_field_2", and "user_field_3". Assuming this is all correct, that will be enough information for someone to migrate the old fields to new fields from your site’s Rails console.
If the plugin’s author isn’t going to deal with this, you’ll likely have to hire someone for the work. Note, I’m not trying to get work here, I’d rather not do it 
Before the migration is done, you should create new Discourse ‘multiselect’ fields that have options that match the values of your old multiselect-dropdown fields. To make the migration process easier, it would be good to use the same name for the new fields as you used for the old fields. That way, whoever performs the migration will know that (for example) multiselect-dropdown fields with the name “NZRAB number” should be migrated to the new ‘multiselect’ field that has the name “NZRAB number”.
I agree it would be best if the plugin’s author took care of this, but if that can’t happen, just go ahead and create new ‘multiselect’ fields and remove the plugin.