i use photoshop to set it outline, the result was positive, maybe you could try to edit the font png file manually. notice that this may required you to spend a lot of time editting each letters from the font. That's what I do to deal with this issues
That's what I did to make the outline (and the reason why I said to add the padding), but I created a script to do it for me instead of having to edit manually.
A way to make the outline manually that's easy is to create 8 copies of the font omg, offset by 1 pixel in all directions (including diagonally), make them all black and merge them, then add the original on top.