That will still have a clear background, just with odd-looking reversed characters in 5x8 (or whatever) blocks.
It won't have a clear background. Did you have a look at the examples on the link I provided?
The examples in the linked thread were using a "positive" pixel method on negative LCD for the big characters.
This would be using a "negative" method on a positive LCD.
You will have large "characters" that span multiple physical lines that
are composed of custom characters that are inverted by flipping all the bits used
in the custom characters used for the larger characters.
But I tried it, and it doesn't work very well. The pixels on the display have too much area
around them (top,bottom, left and right) then because of the gaps between the 5x8 characters
there is too much light.
If you used black electrical tape along the top,bottom, left and right of the pixels
then it is kind of ok, but still not very good.
(It could be done with a glcd)
I think the easiest option would be to simply replace the lcd with a reverse one.
They are pretty inexpensive. < 10$ USD if it is only for a one off project.http://www.ebay.com/itm/2004-20x4-Characters-LCD-Display-Module-Blue-Blacklight-/160797755014?pt=LH_DefaultDomain_0&hash=item25704b0686