You don't say which library or what hardware you are using.
The Adafruit_GFX methods handle the FreeFonts in software. If it is important, they could be rendered with the hardware. However you start to lose portability between libraries.
Bodmer's libraries can handle Fonts.
Personally, I would prefer to conform to the GFX style. But I might add some of Bodmer's features.
As a simple kludge, redraw background one letter at a time instead of for the whole string.
The hardware is easier to draw foreground and background in one go. And it provides flash-free rendering.
David.