So when I’m playing Beat Saber, occasionally in the middle of a song the headset lights start flashing. Since the lights are how the headset is tracked, this screws everything up for the tracking in the song. The screen zooms in super close for a few seconds and makes it impossible to see what notes are coming. Especially on the higher levels, this typically results in an automatic failure.

I’ve tried everything to fix this—recalibrating, turning the headset and the PS4 on and off, adjusting the camera height, adjusting the Beat Saber settings, etc.—but nothing helps. I tried researching the issue but only found people suggesting the stuff I’ve already tried. 

Of note, this most commonly happens when there is a switch from one player to another.

Anyone else experience this glitch? If so, what solution did you find?

Well, I had no idea the lights on the PSVR itself could flash, afaik that never happens during normal useage or when setting up. That means it's very likely that it is some kind of error-signal. For example it could signal overheating or some kind of loss of signal or loss of power/current. That could be something to investigate.
And it's possible (but not very likely) BS is triggering this error-state due to a glitch and not the error actually occuring.