Squaring the Map

Have I posted before about these attempts at creating a square-format map of the U.S.? I think I have, but I'm not sure.

I saw this version recently. The data it relays is not the point of this post:

As a person from Minnesota who has relatives in Wisconsin, the thing that immediately irritated me about it was the way Wisconsin is bumped up above the U.S./Canada border, and therefore above Minnesota and Michigan. What?

Of course, it's not possible to place the states on a grid because they're much too irregular, so compromises have to be made. But are better compromises possible?

Here's my suggestion, at least for the Northeast/Midwest:

The Northeast is pretty much impossible. (Yes, I know Vermont is not above New York.) And that still doesn't deal with the fact that the Carolinas are bizarrely arranged, Washington, D.C. is off the cost of South Carolina, and Texas, Oklahoma, and Kansas are wrong. Although I have to admit, I kind of like the idea of Texas as equal in size to the other states and only being accessible from Oklahoma.