I've just added a third format option when exporting your character's image in HM3 -- "PNG (transparent 400x600)". This is basically just adding in an option for the way it used to be.
When you click it, the size gets reset to 400x600, the Area gets reset to "Character", and all other options are grayed out since you can't make any of the other sizes or head shots export with transparency. Choosing regular old PNG or JPG turns them all back on, though.
This should help those, like DiCicatriz, who use the characters with transparent backgrounds to paste into an image editor for either larger group shots, or just to have in a custom setting.
Let me know if you run into any problems using it. All other options will continue to export with a white background.