Hmnm... compliment mode is by far the fastest way to do it.. but you could have two bitmaps, one which is 2 pixels wide and the height of the screen, and one which is 2 pixels high, and the width of the screen.
Before drawing the lines, blit the left-line current contents to the left line in the vertical bitmap, and the right line current contents to the second line of the vertical bitmap (1,0). Do similar for the horizontals.
Make sure you allocate the bitmaps with your windows bitmap as a friend to ensure they are in the same format, and you can set displayable to keep it in video ram so that under P96 or CGX the graphics card blitter can be used. Just do an AllocBitMap(), then InitRastPort() a previously allocated rastport structure, and attach the bitmap to the rastport.
This should be quick, and not too memory hungry.