Hmm...You could try the following;

Create 2 copies of the text buffer.
Shift copy A 1 pixel right and add it pixelwise to B.
A down and add to B,
A Left, add to B.
A Left, add to B
A Up, add to B
A Up, add to B
A Right, add to B
A Right, add to B.

8 * 4096 = 32768 integer additions per screen (fast). Anything non-zero in B is to be burned, so that adds 4096 simple compares per screen.

Hmm. Quick gimp mock up, achieved by manually following the above process with multiple offset layers in 'lighten' mode.



Note that I inverted the original to show the contrast. In reality the mask ends up inverted against the background image and the original stays non-inverted. I suppose I could have imported a visual background and done it right, but I couldn't be bothered.