Get a 6X scope regardless of AO. Set it at 30 yards and go shoot. The real parallax problem is with higher power. 6X is about right for 5 yards to 150 yards.
You have set a tough group of requirements to meet. Fixed power scopes with BDC or Mil dot reticle seem to be rare. I have the same problem that you do. I never seem to have the AO set properly for a short range shot when I need it. I ‘ve gone to a peep site on my “snake charmer” for close shots. Setting the depth of field ( or parallax or focal distance) on a fixed power scope is easy. I set my fixed scopes at fifty yards. leapers sold a fixed 4X with Mil dot at one time but I haven’t seen any for sale in a while. My preference would be for a fixed 6 or 7X Mil dot if I could find one.