I'm researching whether this function, "add Bluetooth ability to any non-Bluetooth audio source", can be done by only using an iPhone with an existing iOS app, accepting audio input from the phone's minijack input and exporting it using the phone's built-in Bluetooth capability.
I have searched for "iPhone audio throughput app" etc. on Google but can only find DJ apps without the required functionality (and of course these apps are bloated when considering my simple scenario).
Such an app would require that the audio input and output can be set to different sources. I don't know whether iOS supports that. E.g. in my testing, GarageBand does not seem to distinguish between the audio input and output sources.
Also, the cable would have to be four-conductor (TRRS), similar to the Pioneer Cd-V150M, with the extra contact segment allowing iPhone audio in, as opposed to output only. There's presumably "no recognised standard" for such cables, so it's hard to research which cable, if any, provides stereo input to the iPhone. This article implies that Apple's "CTIA/AHJ" implementation is mono only: "one conductor point (...) for the microphone".