How to design a large 125kHz loop antenna for long range RFID application?
Stop doing 'as many turns as I can allocate' and start doing 'the right number of turns'.
As the loop gets larger, the self capacitance and the inductance increase quicker than you think, and you don't need as many turns.
Start with one or just a few turns of your target size, and see what capacitor is needed to resonate it down to 125 kHz, or see what the frequency is for your target capacitor. Then calculate the inductance, and increase the number of turns by the square root of the ratio. You will need to iterate again, as increasing the number of turns will have increased the self capacitance again, but it will get you closer. Rinse and repeat, until you get a capacitor size you like.