The values you get are strange.
The BUSY line seems to work, as the Power Off time is close to the value I get with my 4.2" b/w.
Power On should report a value in the same range; the value should not depend on external conditions, but you could check (measure) supply voltage on the pin-holes at the other side of the panel.
Time for update should be ~4.1 seconds; this is only dependent on the waveform table.
You could change the timeout value for a test in the method _waitWhileBusy in file GxGDEW042T2.cpp to 20000000. If this works, then your controller may have a different waveform table stored in OTP, e.g. for the 3-color e-paper. This would also explain the bad picture.
That's about all I can think off from distance. Of course I don't know the quality of your vendor and the history of your display.
The vendor seems to be Waveshare. I do not doupt the quality of goods from Waveshare.
You could also post a picture of the backside of your display, just to make sure it is a b/w display.
Do I see some red shade on the picture you posted? You can try with GxGDEW042Z15.
Jean-Marc