Hello Johan.
I suspect the Q factor of your "new coil" is too high (>>60?)
If the Q is too high, the OOK of the request for "Page 3 will being badly demodulated and even corrupted...
During the Transmitter encoding it gets turned/modulated on/off. During the "off" gaps, the Resonance artifact in the Transponder will not let the received OOK video envelope fall down to the the lower logic threshold decision point
Therefore for the 15 mS duration of the "Write Request" the tag never sees a meaningful 1>0 transition...or when very close they will blurr into one steady state logic 1 and be contigusious to the 25 mS Charge burst.
Your symptons seem to suggest that as you get closer the Tag begings to "think' it is seeing only one "long continusious Charge burst"
Apparently the tag is designed to "kill itself" if no (or a corrupt?) Write Request is received...the tag empties it's energy storage and prepares for a new "clean restart"...not sure but I think the Tag emits the 16 Pre-bits then discharges it self...a "last gasp?"
Your Oscilloscope view of the OOP modulation "show me Page 3"...in the last 15 mS of the Readers interrogation, seems to show oscillatory overshoot or "ringing" this being symptomatic of an under-damped resonance...ie the Q factor is too high and needs a new damping resistor...probably about 4.7K try to start with?
Also note, the next critical time line event is/would be the identification of the first "bit" of the Start byte....a very high Q will intrude into it and confuse the FSK decoder in the Reader.
I be interested what happens when you "re-dampen" your new coil.
Kind regards
Ray