Do you wanna take the Grados outside? You know that they are open? I do take my SR60s outside from time to time but everybody passing me, can hear what I listen to.

From a power standpoint, every Bluetooth AMP should be sufficient. As Grado can't change cable without modding, no need to look for a balanced AMP either.

Fiio has a great reputation for products over the last 10 years. So you should be doing fine getting a BTR5. I would choose the BTR7 solely for its 4.4mm output but that is not a think with the Grados as mentioned.