Hi Mike,
It doesn't sound like a linkage problem because neutral is not next to 1st. When you are going 60mph the car should refuse to go into 1st for self preservation. Sorry I don't have any good answers for you. It may be a long shot, and I don't know when they started, but most transmissions are now computer controlled. If yours is, you can reset the computer by unhooking the battery for a few minutes. Always unhook the negative cable first, then the positive. Reattach in opposite order. Wear safety glasses whenever working with the battery. Again, I can't tell you if it is even worth trying.
Good luck!