"""I've moved the shoe from the front of the cleat , all the way to the back of it, with no relief in sight...""

I'm not sure what that means. Do you mean you've moved the CLEAT back further on the SHOE?

In any event, the cleat should be positioned to place the ball of your foot either directly over the pedal axis, or SLIGHTLY forward of the axis. If the ball of your foot is behind the pedal axis you risk straining your Achilles tendon.

What kind of pedals/cleats are you using (SPD, Look, Time, other)?

Pedals with a large platform are least likely to cause hot spots. But many strong riders use SPD pedals/cleats without problem. The key is wearing shoes with good stiff soles.

""Chainwheel""

"

My experience is not to move the cleats, assuming that they are properly placed on the shoe with the ball of the foot over the centerline of the axle of the pedal. I advocate practicing different ways to pedal. I vary slightly the way I come down on the push and on the pull. It's hard to explain, more easy to show how. For example, if I bring my heel up higher at the 12 0'clock position, there is less pressure on the ball of the foot than when my heel is lower at the 12 0'clock position. Of course you need to coordinate the pull action with the variance of the push action. But I have had much success on 100+ mile rides in hot weather by going through a sequence of slightly modified ways of push and pull using different angles on the down stroke and pull up of my pedaling. I also agree that shoes that are even slightly too tight will produce painful results.
Hope this helps.