Any advice on how to replace a corroded area housing the petrol cap without buying a whole quarter?

Rubbing back the affected area and filling possibly? 
As long as it is not within a certain distance from a structural part of the car and is not too large then this repair should be acceptable

Maybe a compound polishing lotion, with polish drill?

Glad you mentioned this my 2010 has a few rust bubbles around that area so possible common fault. Located a hole inside the petrol cap and my garage sprayed anti rust inhibitor in there and sealed up the hole with some bonding..I am also looking at how to remove these