Read AS3953 NFC EEPROM when the chip is not supplied
I'm in a similar situation (AS3953, ATtiny85, SPI) and asked AMS for support.
They suggested to use transparent mode (26 13 08 00 as the configuration word) and a phone should be able to read it.
My phone does not.
And my reading of the datasheet would make 26 13 18 00 transparent mode.

Anyway, this might work for you...give it a try.