The max_interval won't have any effect unless you make it too small. It is a protection against the temperature measurements failing. If there is a gap between samples > max interval then it locks the integral, so when you are seeing integral locked flashing that is because it thinks the gaps between the samples is too big. I think it sets the output to the manual setting but not sure. Whatever, you should set it a value larger than you ever expect between samples.
Integral default only has an effect on node-red restart or full deploy, it sets the initial ouput if you happened to switch on right at the setpoint. After that it has no effect.
That graph suggests that maybe the integral should be down at about 15 seconds.
When tuning stick to the step change in setpoint (or power up) as it is much easier to see what effect the tuning has.