Welcome to the Asana Community Forum @Heather_Stringer 
In terms of multiple-assignees have a look at this feedback request thread: Assign multiple assignees on one task
People custom field was introduced recently which might help you: Assign multiple assignees on one task - #634
Now the thing is you would need a paid plan.
Another option could be assigning the task to the main person and subtasks to the other people involved. Again things could be automated with using rules but they are a paid feature also.
You might wanna consider just having one project where you store all your wholesale contacts and everybody has access.
Now you could then link this to google calendar for example and share the calendar with your team so they have these events showing too.
Now for this you‘d have to use an app as at the moment due times are not showing in the calendar. If you do not need due times then that works since they show as full day events.
To fetch Shopify data into Asana there are various ways on how to do this, depending on what info you need and how often or if automated.
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cvs import could work
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Various apps offer a connection also such as:
Zapier, Automate, Make, Appypie
I hope that helps