I should mention also that each bedroom has its own cold air return and they are the size of a normal vent. In addition the large areas of the house also have returns. So overall return flow should not be greatly affected.
Thanks

I used a portable unit in a room with a window like yours.

I removed the screen, cut a large piece of plexiglass the size of the screen, cut a hole in the plexiglass the size of the exhaust hose, then inserted the plexiglass into the window where the screen fit in. I used some small nails to hold the plexi in place, then I caulked the hose flange to the plexiglass and attached the hose.

This worked well, you couldn't even see it with the drapes.

Porting the exhaust into your central AC system will make it work much harder to cool the air. A professional in this field should chime in soon.