Tack on numerous tags around the circumference, pull gently in a circular pattern, moving towards the center. Patience and finesse (as you've learned) is paramount. Once you get the metal moving, it will suddenly pop on you leaving you with a high spot (or several) to tap back down. Use a blunted punch, tap gently until you get it close.
I use Guide Coat to sand down and find high/low spots. Tap down the highs, fill the lows. These tanks are not as stiff as people believe and the metal moves easily once you get it to "understand your intentions
".
Some people might suggest using compressed air, but I dislike that approach completely. You are more apt to balloon the tank than solve this problem. Others have had success heating the the dented area, then applying ice/cold spray immediately to the metal. Cause the metal to expand then contract rapidly. Again, not a fan, but some make it work...
A last option is to use a 3/8 round stock. Bend a 90* tip in it, about 3-4" long. Put a heavy grip on the other end. Use the bent tip inserted into the tank to "push" the dents up. You'll need a bit of slow arc to it so the tip reaches the underside and the rod levers against the filler neck. Careful not to push the filler neck in while leveraging against it. That method works really well (Paintless Dent Removal approach). I've done heaps of tanks that way.