I have now been running for several days without any lockups / crashes, and there’s no way I would have made it this long with the original Ethernet module, so the W5500 / new firmware version seems to have resolved my frequent crashing problem! I will continue to monitor for problems and update this forum if anything changes, but right now I’m feeling pretty positive about the W5500.
The other thing I’ve noticed is that I no longer get periodic timeouts when I run continuous pings. This doesn’t surprise me, because the hardware TCP/IP handling should be pretty close to bulletproof when it comes to seeing and responding to pings, but it’s yet another sign that the new module has improved Ethernet communication reliability.