I'd take a sig gen and resistor and modulate the resistance seen by the DMM by a very tiny amount, at the rollover value. With a LF sine or square wave maybe.
Causing the DMM some jitter, example reading 1.0005k to 999.90 so it's at going back and forth centered at the rollover/range/exponent change, at say at 1Hz.
If Brymen firmware doesn't use proper semaphors, the read and write of the reading data structure would not be atomic.
I'm saying (as a guess) the BT thread reads shared memory holding the last reading, but while the DMM thread is updating it with a new reading- but decimal pt has moved.
Or the BT module messes up reading the long term verses short term average the DMM has and switches between. Just giving some ideas of thing to flush it out, instead of waiting for it to appear.