Johan...
Battery placement and Device Docking Cradle are to blame for all this.?
You are Data logging = why else is battery there in first place?
Battery too close to RFID coil ? = you say lowers Q ...yes, like a shorted turn you reason?...is not 20 still too high?
Battery too close to RFID coil = me say minute charge/discharge battery currents magnetically coupled back into to Reader coil
Magnetic feedback creates "strange forced damped oscillations" in between the Reader transmit gaps = your top picture = plucking plus feedback? = superposition
Close proximity of Reader coil curiously/predictably "dampens/absorbs" this spurious feedback energy...still a vestige = your bottom picture
Why you go to 24mm diameter coil = k factor between both coils now bigger over original small PCB inductor instance.
Why you go to 24mm coil= surely not for more range, SMD inductor is adequate for 2.5-7.5 cm ?...
Why you go to 24mm coil = is your device like an electric tooth brush which gets "docked then manually decanted?..seemed like a good idea at the time?
Your Reader is not endlessly Polling otherwise your device would be successfully read and decanted as it came closer....and you be non the wiser about <2.5cm range?
Has any one else experienced what you are recounting here?
When you enacted the "internal Tag tuning" was the tag well away from the reader?...but close enough to get clocking...on the verge?
Me still think Clock definition confusion due to bifurcation is still a main item here see above.
Could you move the battery and go back to small aperture SMD ferrite coil?...the physical form of your device maybe brought all this on?
An interesting problem here...if it eventually though turns out to be a strange firmware matter, I will be surprised.
Regards
Ray