@yeka already had a few good ones, but failing those,
Is it possible to pop open the reader to see where the antenna lays.
OR
With your Diagnostic Card, the HF antenna runs the perimeter, can you use just a little bit of the short edge to work out where the readers antenna is, so you can then focus your attention with the xFD. (it is not as precise as the xFD, but it will give you a pretty good idea.)
Also
I think that is a good idea, If it can read a card, and a Flex but not the xM1 it will almost prove that it is an xSeries range / reader output power issue, and hopefully we can come up with a solution for you .
If it doesn’t work on the flex, it may be a very low power reader, but doesn’t sound like it.
It could be a data write issue or compatibility issue. (detects “magic” mifares 
)
Do you have gen1a or gen2 ?
Did you TagInfo?
Wanna share?
SORRY IF THERE IS SOME EGG 
SUCKING IN THERE.
I just want to make sure we cover everything off.