I tried overriding a file in includes/modules/payment with a similar file in includes/modules/CUSTOM/payment. The change didn't "take."
There's a twist here: the file is paypalwpp.php. Now, I don't have PayPal Website Payments Pro enabled in my orders total, but modifying this file does make some changes (it seems to define the text next to the PayPal logo during checkout).
So, are my overrides being ignored because this module is disabled? And somehow, it's picking up the text formatting anyway?