Departure gradients are based on OEI, hence why you will meet the gradient with AEO in most cases. I don't recall seeing a procedure that has a climb gradient for AEO. If you can't meet the gradient on OEI, you will need an EOSID.
Your thr red/Accel height of 1000ft meets the minimum of 400ft, so yes, it's operator defined but meets regulatory standards. For airports with NADPs you will need to modify that if your operator standard doesn't meet the NADP (our case, Colombian airport with Accel height of 3000ft agl)