Clear out on Jost - clear in at Cruz Bay STJ - move to your desired anchorage for a day or 2 - clear back in at West End to go to Norman Is from STJ.
Get the proper info and forms from Moorings office before you leave.
Time spent in clearing - out-in -in - depends on busyness of C&I plus the time spent getting to Cruz Bay - a few hours combined I guess.
Few services of any kind available in the STJ National Park so plan provisioning accordingly.