Yesterday, the BTR3 suddenly started showing up on the FiiO app. Didn’t do anything special, besides what I had done in the previous days trying to fix this. When I finally managed to get a successful connection to the FiiO app the BTR3 was hooked to my MacBook with the USB cable while it was also connected to my iPhone via bluetooth. I don’t know, perhaps there’s a mix-up with Apple’s continuity protocols.
Just to make things clear, the BTR3 was connecting properly to all of my devices via BT; I just couldn't make it show up on the FiiO Music app (and therefore I couldn't tamper with the settings). I am using the latest version firmware and the latest version of FiiO music.
For now I'm quite happy with it's performance on my FLC8s IEMs. I wish Apple would jump on to the hi-res BT protocols bandwagon, the BTR3 itself is certainly doing a better job rendering music compared to any other basic DAC implementation available on my devices.