I'm using 56mm x 87mm (2 1/4" x 3 1/2")premium sleeves from Mayday Games. These are a perfect fit. I can't see these decks getting as much use as my C&C Napoleonics and the Great war ones seem to be of good quality so it really depends on how much you plan on playing the game. I'm glad it's not just me that gets the two decks muddled up and your "half and half" idea is a good place to start!
They explained everything in detail and at great length. After they finished I sat, despondent, contemplating a bleak and empty future. "I’m glad you’re depressed" said one. "It means you’ve understood the situation.”
I used the purple Mayday sleeves (56mm by 87mm) too - they work a treat.
One pack does the whole game which is nice (unless you also sleeved the four villain cards in LEGO Batman in which case you'll be a couple of sleeves shy of what you need..