Nah, that won’t work. The UID of NFC chips can only be changed if they have a Chinese “magic” backdoor feature. AFAIK there are no DESFire chips available with that feature.
Even if they were available, you would not be able to use your NExT because the HF (13.56MHz) side of the implant is an NTAG216, which is a completely different chipset that is also not cloneable. The only part of your NExT which is has a changeable “UID” is the LF side (125kHz) because it uses a T5577 chip, which does have the “magic” backdoor feature.