I do have some systems that appear to have overheating problems. Is there a
repair I can do to stop/lower the chance the system will overheat.

Technically, the system doesn't actually overheat, especially if it was played
in a desirable environment. But the drive was simply not suited to operate at
the internal temperatures that the Gamecube is expected to operate at.

The Gamecubes that give the disc read errors do it immediatly on start-up.
Not after they have been running and warming up.

That can be an indication of the same problem at an advanced state.

I've found a few posts referring to adjusting the
alignment on the Gamecube laser assembly, however I have not been able to
figure out how to do this. Any suggestions you might have?

Not many, I'm afraid. As one poster has mentioned before, there are no actual
pots to make adjustments with the exception of laser power. But readjusting
the laser power in this case won't do you much good.

Gamecubes having disc read problems are most likely going to have a defective
optical pickup, and repairing that problem may require replacement of that
part. - Reinhart