Yeah, I think we need to do some more digging.
It sounds like you have to be discreet, so on your door readers, are there any markings, logos, words, colours?
Are all the readers the same?
Can you “google” to find us an image?
Like @Devilclarke said above, quite possibly it is a Dual Freq. reader.
You mentioned the HF LED of the Diagnostic card lit up, but didn’t mention the LF LED…
Did that light up also?
I’m still a little unsure what is going on, especially with he KBR1 reader not working, I am thinking either faulty reader or the Card is a ISO15693 (the KBR1 only reads ISO14443A)
Let’s do some more testing.
Can you do me a favour, could you download Taginfo by NXP ?
Scan your access card, and let us know if you get any results ( feel free to hide the ID )