What is the recommended maximum length of time to leave a soldering iron hot, to prevent damaging the tip?
There is actually no &quot;recommended maximum length of time a soldering iron can be kept hot&quot;, just as you might assume - the longer, the worse.
Regarding the idle time, these scenarios came up to my mind:

manually switch the solder after few minutes
let it go until the tip is gone - maybe you find out it can last longer than you would expect and then just buy a new one
use your solder's sleep feature although it does not work great (as you claim) and live with it
and finally - buy a new solder with better sleep feature.

And last but not least - your temperature of 420 °C is unnecessarily hot, which affects the tip durability a lot.
The tip life decreases exponentially with temperature.
Try to find the lowest temperature that still works for you, to balance the workability vs. tip durability.
JBC has a decent article regarding the topic:
https://www.jbctools.com/blog/correct-temperature-soldering/