as dibble said you shouldn't need a new basket with every clutch pack, but if it's been through a couple of clutches already then perhaps the basket carries accumulated wear marks from the tangs on the friction plates. These prohibit outward expansion of the plates on dis-engagement (clutch lever in) and may promote clutch drag, a symptom you seemed to be describing earlier. You could send in a few snaps of the basket if you manage to take out the plates yourself (keep them in exactly the same order as you take them out),. or if you have little faith in your workshop then seek expert help. In summary it's not uncommon to change baskets with the plates but you shouldn't have to at each and every pack change.
good luck
