Climbing out on racks to fix damaged pallets or mis aligned pallets is extremely dangerous. I think I would be justified in asking for that order to be put in writing before doing it to protect me.
I have never been a fan of double deeps always struck me as a product invented after we had a forklift to sell.
You could get fork extenders but it would be very hard to see them getting in to the pallet and re arranging them. If this is a frequent occurence then it is the pallet's fault and management has to face up to that and buy decent one.Otherwise find another job, your life is more important.