If it were my room I would place the fan in the orange space. Pushing air through a duct that cools hoods is going to be quite difficult, consider the differences of height and reduction of airflow.
A far more efficient way is to place the fan in the orange space. This will move the air from the now passive light intake quite well.
If it were my room I would also reconsider having ANY active intakes at all. I could use the fan elsewhere, why use an extra step for no reason?
KIS
Keep it simple
Do some reading!
https://www.icmag.com/ic/showthread.php?t=112862
Blowing air in...
Reason being....Hot air from the lights cause extra wear and tear on the fan over time.
This is a terrible basis for designing a grow room. Yes, we MITIGATE damage to our equipment but my plants are more precious then an inline fan.
I also presume damage is minimal because I have known growers to have the same fan installed as their light exhaust for up to TEN YEARS. Good inline fans are durable!