Are we looking at the same site ?
TuneECU_Android
In that long page, roughly in the middle, there is a list of bikes on which the Android version of TuneECU works.
About a third of the way down that list is the Rocket III, with a red asterisk -- I totally missed the first time around.
Yes, I went with the LX BT adapter, only because of the ones on the list, that one was the least expensive -- around $50 on Amazon.
When I was all ready to load
@HansO 's tune and it wouldn't work, I was about to send Alain a nasty email, when I looked again at the site, and saw the red asterisk notation at the bottom of that list: "* With Bluetooth connection, reading and reprogramming map functions are not available."