NExT both working and not working with HID readers

What do you mean by “reject”, Are the readers complaining about the NExT? If the problem is that you can’t get a read, I’d recommend trying to locate the coil with a field detector keychain.

Also, try this:

Have you tried scanning your badge with TagInfo? Most phones are HF only so this could give you an indication if the badge is dual frequency or not.

Also, use the diagnostic card to check what frequencies are enabled on the readers. This should also give you an idea of the duty cycle of the reader.