If you need to get to your new resort early in the morning to get your package stuff (tickets, dining, etc.) then a taxi over is the best bet. (However, that will involve lots of tipping). (Taxi driver, bellman that stores your luggage at WL, and bellman that delivers your luggage to your room at WL).
Personally, I would just let Disney deliver the luggage. Since you are at All-Star Music, you can call Luggage Services the night before and schedule a pickup. Then leave your luggage stacked by the door. They are not a tipped position, so no tip is necessary, but they do appreciate something. Then one of you can take the taxi over to WL and get the package stuff and meet the rest of your party at a park.
Then when you get back to WL that afternoon, call for your luggage.
If you don't need to get to WL that morning for package documents, then just schedule a pickup, leave the luggage by the door and head on to the parks, when you get to WL later that afternoon and check in, call for your luggage.