Let's assume I am traveling down the road in 5th gear at a steady 60mph. If I shift into 4th, maintaining 60mph and the same amount of throttle, will my mpg be affected by the increase in rpm?

 

Yes

 

This car gets best mpg by keeping it under 3700 rpm.

 

between 3400 to 4000 rpm... you want the front valve to open ... it is around 3200.

It is 104 km/h in 6th gear - the power is more and I assume that extra 100 rpm will make the fuel burn better and I assume it will be better fuel mileage

It is a mere difference between say 12 L/100km to around 11.2-11.5 L/100km not big.

I think you might have no fun driving at 60mph (96kmh) on 5th is actually ok.