Some people emulated 125 kHz-RFID-tags with just a coil connected to a small 8-bit µC. Does that theoretically work for 13,56 MHz Mifare-Classic in a similar way? May be with some additional passives to realize the load modulation? If I get it correctly there are much more clock cycles available compared to the 125 kHz version. The 847.5 kHz subcarrier may generated by hardware pwm.