"Every rule that I’ve read speaks to what should happen in the case of double qualifications.
Does the double qualification rule for state competitions extend for additional invites? I.e. If a state has a team that triple qualifies do the highest 2 ranked skills teams receive invites? Or does the state have freedom to invite outside of the skills ranking after the first invite?"
No, the state does not have the freedom to go outside of the skills rankings. In the case of a a triple qualification (or two or more teams double qualifying), the states/regions World slots would go to the next highest skills scores posted in the state for the season until the number of slots are filled (among the teams not already qualified through the state/region competition).
For example, if the automatic qualifiers from your state/region are Excellence, Champions, Finalists and Design and the Excellence Award winner was a finalist and the Design Award winner was a champion, then two spots would then be filled from the state skills ranking among the teams not one of the automatic qualifiers above. Also, note if one of the teams was in the top 50 Skills scores in the World, that does not give an extra qualification spot to your state/region. That spot is totally independent of the state/region qualifications.