Although this is not a 250 quad (motor-to-motor diagonal = 400mm) I followed the suggestions from @Leonardthall for smaller quads I now have a pretty good tune.
Values used:
AUTOTUNE_AGGR, 0.1
AUTOTUNE_MIN_D, 0.0005
MOT_THST_EXPO, 0.6
MOT_PWM_TYPE, 2
ATC_RAT_PIT_FILT, 20
ATC_RAT_RLL_FILT,20
INS_ACCEL_FILTER, 10
INS_GYRO_FILTER, 40
Autotune results (incl. payload):
ATC_ANG_PIT_P and ATC_ANG_RLL_P maxed out at 18 and I reduced it to 12.
Roll PID values were 50% of the pitch values. It flies better when using the Pitch PIDs on the Roll axis as well:
ATC_RAT_PIT_P 0.08163819
ATC_RAT_PIT_I 0.08163819
ATC_RAT_PIT_D 0.00409838
ATC_ACCEL_P_MAX 177842.7