It will be very challenging to be discreet for OP, I think.

The three pieces OP want to carry on are:

1. purse ("My purse is fairly big - it also contains my laptop computer", "My laptop is just barely too big to fit into the camera bag"--see post #3)
2. camera bag-backpack ("The backpack contains my cameras. (I'm a professional photographer) "--post#1)
3. "overhead-size" bag ("My "overhead size" is a roll-aboard"--see post#7)

I don't understand why some folks are trying to calm OP's mind when obviously none of these three items can be downsized or crushed into one another during domestic flights.

Would I chance it, if I were the professional photographer? NO WAY! I would know I had to check at least one bag.

If anyone had seen any passenger successfully boarded when carrying 3 carry-on of similar sizes as OP's descriptions, please tell. So OP can choose such airliners with loose restrictions. At least AA is out. If SFO is OP's base, I doubt UA would allow these 3 pieces either.