Is there a setting that would allow the X3 to stay "on" while it is in the charging dock?
There isn't to my knowledge. On my 950XL there was a setting that I would use when installing OS Updates and or using a podcast app while driving... and that setting was in the "Lock Screen" section that was "Never." This phone's OS doesn't have the "Never" sleep option. However... I'm testing a possible option for you now, I'll get back on the results later.
*** Sorry, thought I was on to something but the "Lock Screen" time out of 5-minutes seems to override any other setting I played with.