I've discovered a way to mostly fix the issues with pieces within welded groups moving relative to one another. This may or may not be breaking news... so forgive if it is not. Movement of pieces in a welded group are relative to the PARENT part, and no others. Go do a test... Place four walls in a room pattern, and add a floor. Place an invisible blocker or target in the middle of the wall group, hovering in the center or aligned to the top or bottom or whatever you think is best. Then, group the walls with the invisible piece. Make invisible piece the parent, and weld. Move this around using some scripts, and you'll likely find that the walls/floor pieces stay locked in place relative to each other. However, there is still a caveat - that the parent piece will move relative to the other pieces, and thus returning a welded group to its original location (as in an elevator car) may still cause misalignment between the car and the doorway. At least you won't have gaps in your elevator car, though! EDIT: my conclusion is that this is not a reliable method for carrying players from one spot to another. small, short distance, simple elevators work. But try to make something go diagonal, fast, or have lots of parts, and it will be unreliable. It seems to be dependent on the host's internet ping, which has been slow at times for me. The higher the ping, the more jerky and unpredictable the movements become. It's a deal breaker
update: I just created a movable elevator shaft which does not seem to adhere to the rules above. The shaft freaks out and falls apart (there are 11 pieces welded). they are set to move to location of a labeled object, rather than #units. One thing I am curious about is whether, (even though it is not #units) I need to uncheck the box "local". That might help... Stay tuned...
my conclusion is that this is not a reliable method for carrying players from one spot to another. small, short distance, simple elevators work. But try to make something go diagonal, fast, or have lots of parts, and it will be unreliable. It seems to be dependent on the host's internet ping, which has been slow at times for me. The higher the ping, the more jerky and unpredictable the movements become. It's a deal breaker