Recommended proximity of HVAC vent to return air
I'm not a HVAC engineer, but your reasoning and theory sound good and well thought out to me.

I strongly believe (until I'm proven wrong) that moving the vent to the other side of the room would make a (noticeable) difference to the room's overall temperature during the warmer months.

Does the same duct-work heat your home during the winter months?

If yes, you will also want to take that into account when repositioning the vent.