Basically, multi-hauling plus bins and barrels causes loads and loads of cancellation spam, because everything useful is getting hauled as often as not.
When hauling a single item, containers should not be used to haul it. If there's one available to put it in, great! But don't take the entire bin to the new pig tail thread and back again; take the thread to the bin, and be done. This goes double if you're already near the item, triple if you're already holding it.
If multiple items can be hauled in, don't take a partly-full container out to them; take an empty one instead. Once back at the stockpile, if the new items can fit into an existing container, dump them all into it, leaving the hauled container empty for another hauling job.
This might be simplified by letting each stockpile have a dedicated hauling container, replacing the empty one that stockpiles currently like to have. While the stockpile has a dedicated hauling container, only one dwarf can use it at a time, but can collect multiple items at once, and won't disrupt dwarves trying to collect something
from the stockpile. If the hauling container can't be emptied, undesignate it, and designate a new container if available, as long as that wouldn't put the stockpile over its limit. (If there aren't any available, this would be a good time for an announcement, though a
self-filling empty container stockpile should make that less likely. It might also help to check first whether one of the stockpile's current containers can be emptied by combining it with another.)
Stockpiles with wheelbarrows should use them instead of hauling containers, multi-hauling as many items as will fit in the wheelbarrow. (Dumping the load into empty bins might be trickier than it sounds, but shouldn't be too hard.)
A stockpile with neither a wheelbarrow nor a designated container, because it don't use any, because it's hit its limit, or because there aren't enough containers to go around, can have items hauled in one by one, as if bins didn't exist, using many dwarves at once if necessary.