Hexfreds are a variety of ultrafast/soft recovery silicon diodes. The original Parabee had UF4007 ultrafast soft recovery silicon diodes. Such diodes have a small, fast reverse recovery spike, which is further attenuated by the reverse recovery spike filter (RRSF) incorporated into the Parabee design. There is no real difference there.
Schottky diodes are even quieter; you might not need the RRSF - but you already have the RRSF, so what's the point? Again, you are very unlikely to hear any audible difference.
Cree does make a 1200v Schottky diode using silicon carbide, which has a bigger voltage margin than the usual 1000v diodes. But the fact that your ancient amps are still working suggests that the margin is already quite adequate. I suppose one might get a warm feeling from increasing the reliability margin.
On the other hand, we have seen a few amps whose PSU filter capacitors have failed in their second decade, which is why we offer the rebuild.