(for what my "limitted knowledge" is worth)

PWN is intermittent DC, I would use DC mode to measure current.

As to make LED brighter without using more current, I think that strays into 'free energy' subject. I don't think you can.

Do a test, DC with varying voltage, adjust to desired brightness, measure current.

Repeat using PWM, adjust to similar brightness and measure current.

I think you won't find a way around 2+2=4. I hope you can but I couldn't a few years back.

Robert