What firmware have you currently tested?
If it's a stock firmware would you mind trying Braiins OS?
I heard that they developing firmware that supports beaglebone except for the Armlogic board you can read more here
Bitcoin Mining Control Board Variations ExplainedIf it doesn't work you don't have another choice but to replace it with the universal one where you can able to flash it with mod/custom firmware like BraiinsOS.