Yes, the 5.9V(no load - when connected to the Arduino it measures around 3.4V, I think) is very odd to me as well. Think I will redo the measurements, although I was very careful doing them last time and repeated them several times to confirm.
I can arrange a separate 5V power supply. Don't you think that 4.8V can be considered good enough for most practical applications requiring nominal 5V?
Do you believe the code has no issues?