Have you tried making the avatar slightly smaller than the maximum dimensions? Also try putting a border around the transparent avatar in the largest allowable dimension but make it the colour of the forum background (C9C9C9).
I created my current avatar in Photoshop with a transparent background, re-sized it so it fits within the 125 x 125 non member limits and it seems to work okay. If I upload the large version without re-sizing it first, it is automatically re-sized and the background fills in white.
Edit: Changed my avatar again
💛 LEANNA DECKER 💛
"TIME TO PUT SOMETHING, BETWEEN ME & THE SUN.
WHEN THE TALKING IS OVER, IT'S TIME TO GET A GUN."