Resize the artboard so that it matches the size of the artwork. Then resize it from the center outward.
I tried that and it does work. Is this standard procedure? Seems like a lot of work.
I don't know if there is a standard procedure. Normally I have to align my graphics manually anyway, because the calculated center often is not the optical center. And of course most of my stuff goes into InDesign - no need to center it on the artboard. Nobody will ever see it.
Why not just Ctrl/Cmd+A to select everything?
If you have specific objects to go together, instead of grouping you may select them and Select>Save Selection so that you can work on them individually and then at any time Select>[Your chosen name of selection] to select them together without moving them from their layers.
Draw a rectangle on a new layer. Align everything to that rectangle.
Select the rectangle and choose Object > Artboards > Convert to Artboards.
Delete any other artboards.