Is there some way to use a 4x20 rather than a 2x40? so the top 2x20 is like the first 2x20 on the 2x40, and the bottom 2x20 is like the 2nd half of the 2x40?
Yep. It’s application specific of course…
What does that mean precisely.
It means that how it is handled will be specific to your application because it isn’t part of the recommended design.
But this doesn’t mean it won’t work… In fact most of the controllers I’ve seen make the addressing work the same way, so it might just work ‘out of the box’ 
Just get the LCD and give it a go
That sounds like a good plan.
The reason i cooked up this harebrained scheme was because i found this beautiful backlit LCD , just gorgeous.
And please tell us how it went, and the model of the LCD