can another plugin make custom content type support custom page extension?

What do you mean by “custom page extension”?

https://www.ads-software.com/extend/plugins/custom-page-extensions/

Ah. No, I have no plans to support that, and the reason it’s probably not working for custom post-types is that WP’s code for handling URLs is a disaster (imo). If you need that kind of flexibility, I would strongly recommend using a different system (MODX does this stuff natively and it is extremely flexible).