I decided to try playing with the tag I have with me (despite my better judgment earlier). I had the same issue, reading was fine but when trying to write, it didn’t have any effect. Then I started playing more generally, did a password check, and bricked the tag. Oops! 
I am assuming that “Block 10” referred to in your json file is actually block 2 on page 1 (the assumption being that if you keep counting after 7, 8 would be page 1 block 0, 9 would be page 1 block 1, etc…).
While digging to see how I screwed things up, it looks like (and forgive me if you already know this) blocks 1 and 2 on page 1 contain traceability data, and that tags generally do not allow these to be modified (but apparently some do?). From the T5577 data sheet:
“Blocks 1 and 2 of page 1 contain traceability data and are transmitted with the modulation parameters defined in the configuration register after the opcode “11” is issued by the reader (see Figure 5-10 on page 19 and Figure 5-11 on page 19). The traceability data blocks are programmed and locked by Atmel®.”
That’s about as far as my understanding goes. And I could be completely wrong. Good luck!