Assuming that you have played musical chairs with boards in slot one, and the problem is at least semi-repeatable . . .
Since the problem appeared with the new chassis, it and the chassis almost certainly are related. The chassis might have a system monitor or power-on reset module that is independent of the POR in the slot 1 bus controller. The time lag feels like a thermal soak. Some power supplies have a POR output signal, a hidden something that might go sideways. Another hidden gem is an AC Fail signal out of the supply. When connected directly to the backplane, it can force a SYSRESET. And finally, the forgotten cousin, SYSFAIL. Any scope with 3 or more channels can capture transient activity on these three utility bus lines.
Who made the old chassis, and who makes the new one? Also, power supply make and model for the new chassis?
And, where are you located?
ak