How to choose the author of a post regardless of the role of the user?

Question

WordPress

Hello!
There is a custom post type and a form for adding / editing this custom post on the front-end (bypassing the admin panel).
In the admin panel, if you log in under the admin account, you need the ability to edit the author of the post, regardless of the user's role, but the drop-down list shows users only with a member account and higher.
Those. I want to show all users in this list.
If a user publishes a post through the front-end, then he becomes the author of the post, even if he has the role of subscriber.
The role of contributor is not suitable for me, because I do not want to allow users to publish blog entries. Through the front-end, all users, including those with the subscriber role, can only publish custom post types.
How to solve this issue correctly, maybe you can still change the output of the drop-down list so that you can assign any user or use some plugins to create a new group of users and allow them to publish only custom posts? If the second option is the most correct, then which plugins are better to use for this and how to assign a new user role during registration in the case of multisite?