AC uses a condenser in front of the radiator, this gets very hot from the 'freon" being compressed, the condenser cools it back down.
So radiator is getting pre-heated air when AC is on, and on a hot day those few degrees matter
I would check that fins are clear on condenser and radiator, they can get clogged up with dirt, bugs and leaves over the years.
Spray water thru them and down in between if possible.
Do you notice any pinging/knocking when AC is on?
Pinging causes overheating, also engine damage
When you say you flushed the engine, did you flush the radiator separately, removed hoses and ran water thru it to get debris out of the bottom?
Build up over the years will clog some tubes in rad.
After engine is warmed up shut it off then remove fan shroud, just two bolts, and move it back.
Now run you hand across radiator fins should be a nice even heat getting slightly cooler at the bottom.
Any overly cool spots are blocked tubes, no hot coolant is circulating there, and time to replace radiator.
With AC off, do you notice that temp gauge goes up a bit when stopped at a light, it shouldn't.
If it does then your Fan clutch could be failing, not fully engaging when radiator is hot.
And one final note, is the engine actually running hot..................
Temp gauge and it's sender on the engine could be off, 2.3l engines have the sender towards the rear of the head, so gauge tends to stay above 1/4 but well below 1/2, you report yours running at about 1/2 way.
Only way to check that would be to get a temp "gun" and check the upper and lower rad hoses after engine is up to operating temp.
Upper hose should be about 185-190degF
Lower hose 10-15degs cooler
1/2 way on most Ford gauges is 215degF
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