I'm not sure how much it'll actually help, but I made a light guide to mount the lights into, then mount them into the sphere. It seems like it'll be easier to glue the lights into these and then let the pins locate the correct spot rather than trying to do both things at once in such a cramped area. Credit to @RyanSchriten_1692145 for the idea.
https://www.printables.com/model/1009961-light-guide-and-jig-for-epcot-spaceship-earth (edited)