Several things I have found with shoes is that if they are too narrow, you will get foot soreness, and if the depression for the metal plate that locates the cleats is too deep, you will get foot soreness or hotfoot (because those small bones behind the toes, the metatarsals, squash together and play havoc with the nerves that run through them). And, if the cleat is tightened down too much, you will get the trap on the pedal pushing harder against the plastic sole... and have some difficulties clipping in and out.

The first is not really fixable unless you get new shoes; you might try wearing thinner socks or none at all to see if that works. The second may be fixed by sliding an old, expired credit card over each depression, maybe taping it in place and reinserting the insole (Specialized take care of this with their BG sole inserts). The third may be fixed by loosening off the cleat screws and inserting very thin washers or spacers between the sole and cleat. This design of pedal gives you float, so that's OK, you just need to be careful not to create too much space so you get vertical movement on each pedal stroke.

I find it quite stange that you should get foot soreness after such a short time despite the Eggbeater design and their lack of platform.

As a by-the-by, I was doing research on an old Shogun that I have that is now FG, and like your Miyata (I presume) it was made in Japan. There was an archived discussion on the Shogun model and consensus was that they are very nice frame. I think I can understand the charm of the Miyata with its skilled Japanese assembly.