Ok,
you can do something like this:
- create hidden field available on registration, and assign your value via URL
- create custom plugin to copy this value from hidden field to store_id field

How to create this plugin:
- Download, install and enable our skeleton plugin, you can download the code at the end of page https://www.easy-profile.com/docs/44-triggers.html
- Edit file /plugins/jsn/skeleton/skeleton.php
- Remove examples functions: triggerFieldAvatarUpdate, triggerProfileUpdate
- Add this function:

triggerProfileUpdate($user,&$data,$changed,$isNew){ 

  if($isNew){ 

    $data['select-alias-field']=$data['hidden-alias-field'];

  } 

}

replace "select-alias-field" with alias of your select field and "hidden-alias-field" with alias of your hidden field.

NOTE: this code is for example purpose, not tested and not supported

docs at: https://www.easy-profile.com/docs/44-triggers.html