Remember that there are commissaries and staffed camps available, so you area not really that far from help and small stores.
Our 12 person crew took
-one small roll duck tape that we did not use
-one Thermarest repair kit since all the adults were carrying Thermarests. We did not need to do any repairs
=> I have had valves fail but never a puncture, even when I stepped on my pad with my crampons (lucky me)
-two tent pole repair sleeves
-one small sewing kit (the kind hotels used to give you for free). Some of the Dry Ducks clone rain gear we had started to fall apart, so we did do a bit of sewing