Well the good news is ( To me at least ) everything sounds like it is done correctly.
Quite likely, and one of the great things about the NExT implant is it’s size…unfortunately this results in a reduced read range.
Often it is the reader that is out of our control to improve, they sometimes are not putting out enough power to couple with a tiny xSeries implant.
Which leaves you with a few options.
First Try using your Diagnostic card on the reader, 
the LF LED should hopefully light up…or it may blink. Either way the brighter the better.
Let us know how that test goes
Then,
Use your xFD to locate the antenna and therefore the optimal placement of your NExT when trying to read it. again brightest is best,
if you have no luck initially try moving it slowly ( especially if your Diagnostic Card was flashing rather than steady)
Incase you weren’t aware, you want to be presenting your NExT ( and xFD when testing ) perpendicular to the antenna like this
just like on your phone when using the HF side.
I have also had some readers that I have struggled with also, but by doing a “swipe” method rather than just a “present” method, I found this improved my chances of a successful read by a huge amount.
Swiping it across the face, something like this
good luck and I hope these tips work for you
alternatively
You could a different implant with increased read range, something like the FlexEM in your case, which will be a larger implant but with the larger antenna comes better performance with stubborn ( low power) readers.
Also for you to consider would be the:
FlexMT
FlexMN ( If there are any left in stock )
FlexNExT ( currently undergoing redesign )
Let us all now how you go and come back with any questions 