Usually if the derrivative part is too big, it crashes the system. That is what i know from dynamic systems control. Derivative part is what gives it the responsiveness, makes the system react faster, but too much of that isnt good coz it can easily crash. All your derivative coefficients look kinda too big to me. Just as a note, i personally I dont use pid for extruder in reprap, coz i think its overrated on the account of PID name which is usually a very neat thing. But our pid is not actually pid, coz is implemented via pwm which is brutal and kinda defeats the main objectives of using pid, which is smoothness and stability. Using a DAC and a system to go with it like that is more complicated, but better in terms of smoothness, and i guess thats why the name is appreciated, but again thats not our case.
Change config.h of whichever firmware you use to use bang-bang instead of pid. Also in config if there is a PWM setting, make sure its 255 (not 170 or such). If you use bang-bang and problems are gone, then you can confirm that it is not about shorts and it is just about pid values. Imo should still check for shorts, aint that hard, and may be well worth the time doing it.
If it all is ok and it is only about pid values alone, could easily change the starting pid values in config.h. There are many approaches for this. Tweaking pid values is more of an art than a logic procedure, and you have to test a lot. My suggestion is to start with a PI only controller, that is to have derivative part = 0. Put like 2/3'rds in proportional coefficient and 1/3rd in integral and check if that is stable, e.g. no fluctuations or temp swings (if swings, decrease integral in favor of proportional). A PI regulator is capable to hit the target, but its slow, thats where derivative part comes in: derivative part increases the responsiveness of the system, makes it faster. Take some from the integral and put it in derivative, keep doing that and test the system untill the system is responsive enough, e.g. heats up in ~3-4 mins, but still does not overshoots too much e.g. not more than 4-6-8 degrees (at first target hit), and on top of all that, is responsive enough to deal with plastic flow.
Change config.h of whichever firmware you use to use bang-bang instead of pid. Also in config if there is a PWM setting, make sure its 255 (not 170 or such). If you use bang-bang and problems are gone, then you can confirm that it is not about shorts and it is just about pid values. Imo should still check for shorts, aint that hard, and may be well worth the time doing it.
If it all is ok and it is only about pid values alone, could easily change the starting pid values in config.h. There are many approaches for this. Tweaking pid values is more of an art than a logic procedure, and you have to test a lot. My suggestion is to start with a PI only controller, that is to have derivative part = 0. Put like 2/3'rds in proportional coefficient and 1/3rd in integral and check if that is stable, e.g. no fluctuations or temp swings (if swings, decrease integral in favor of proportional). A PI regulator is capable to hit the target, but its slow, thats where derivative part comes in: derivative part increases the responsiveness of the system, makes it faster. Take some from the integral and put it in derivative, keep doing that and test the system untill the system is responsive enough, e.g. heats up in ~3-4 mins, but still does not overshoots too much e.g. not more than 4-6-8 degrees (at first target hit), and on top of all that, is responsive enough to deal with plastic flow.