How to enable registration on sites within my network? W/o redirect to main.

I want to allow my clients on my network to have visitors register on their site. Currently, there is no link or button to allow visitors to access the signup page. This looks like default functionality for some bizarre reason. Anyone trying to reach “subdomain.mydomain.com/wp-signup” is redirected to “mydomain.com.” The same occurs even if the client is using their own domain name. (subdomain.com/wp-signup)

Instead, visitors should be able to register on the subdomain, and remain there, without ever seeing my domain.

So far in my research, others have recommended Multisite User Management, however this did not do what I needed. I don’t want any manual involvement in the user registration process of my clients.

Currently, my best lead on a solution came from here. From this I’ve replicated the signup form on my main site. This includes the site creation form, which should not be on a sub-site. I need to prune out what I don’t want, but I’m not familiar with WP’s code yet. It’s a major challenge for me.

I’d appreciate any help with this. Let me know if I need to share my code.

My Goal: For registration the subsite should behave as if it were a stand-alone WP installation. Anonymous visitors register on subsite without being redirected to main site.