Since you did not tell the version we assumed the current 1.4.2. Zenphoto 1.2.1 is ancient and we can't support such old versions (we don't release new ones for no reason).

So before we talk any further, please first upgrade. (btw, if your server is too slow "visual thumb selection" should be off by any means).

Is there a file I can edit in 1.2.1's zp-core folder that would remove the images from even displaying in the first place in album edit?

I'll upgrade, but it's not something I can do at current.

As mentioned by acrylilan--we do not support such old versions of Zenphoto. You need to upgrade. Specially given the security vulnerabilities of such old software.