One of the many things that 4e does right is fix that. Move one square in any direction, and it costs 1 square. Just adjust for terrain (difficult costs 2 per square), and you’re done.
So here’s the thing.
You don't need a grid any more!
Read that again, and let it sink in.
Just grab a ruler to measure the inches, and your minis can move anywhere, however the heck they want. No grid needed. Count each full inch of difficult terrain as 2 inches, and move front-of-base to front of base. Go ‘round corners by following the path, and allow free movement of 1” for the shift - the old 3e 5-foot step, reborn.
Getting rid of the grid means getting rid of the battlemat and boardgame mentality. It means that grey tablecloth (the one you washed with your socks by accident. Yes, that one) is your dungeon floor, with books marking dungeon walls. You’re out of Boardgame-land where you’re counting the movement and firmly into Wargame-land with all that entails. Freedom of movement, tactical use of terrain and pure, unadulterated old-school D&D goes back to it’s Chainmail roots fun.
He's got a number of intriguing options that this makes available, including a neat idea for miniatures. I'm not sure they're all worth trading in the ease of counting squares for wrangling of rulers, but I have to admit, I like not feeling trapped in a grid.