Overall, your position is untenable

Most of your argument hinges on the role of the DM in the group - you specifically cite p.5-6 of the PHB. However, this defines the role of the DM within the group: at issue is the composition of the group as a whole and the DM has no special role or authority in that.

The formation and ongoing evolution of a social group is the prerogative of the group members (and prospective members) individually and collectively not the rules of the activity they intend to engage in. For example, the rules of a football association (written and unwritten) are not the rules of football - for one of the members to assert authority because they act as the referee on the field is a category error. Similarly the social rules of a D&D group are not the rules of D&D.

In particular

Inclusion of new members of the campaign are group decisions.

Indubitably - see above.

Introducing new characters towards the end of the campaign disrupts the narrative.

It all depends on how this is handled: maybe yes, maybe no. There is probably a great question on its own in this one statement - please ask it but please read good subjective/bad subjective first.

By making an executive decision under DM purview from the get go, I am undermining their perspectives and feelings by "laying down the law" and not listening to their side. (This might be true.)

First, the decision is not within your purview as explained above. Second, there's no "maybe" about it - this is absolutely what you are doing.

The player is part of the pre-existing group and is not a new member as this adventure is an extension of main campaign.

This is the best reason given for including the player but is not a compelling reason on its own.

While players are encouraged to add to the narrative, what is and is not narrative appropriate falls under the domain of the DM as stated on pages 5 & 6 of the 5e Players Handbook.

Really? Go read those pages again because they say no such thing. Those pages describe a dialog between the player's and the DM from which a narrative emerges. The DM controls the environment the players control the PCs - you need both to have a narrative.

Notwithstanding - see above.

Additionally, I have interesting narrative plans involved with his character, that several players and DM's outside of this group approve of.

The first part of this is the second best argument for inclusion. The second part is an irrelevancy - people outside the group don't matter (including me).

As the DM, I serve as referee. ...

See above.

As a DM I have a prerogative to enjoy myself during these sessions else I lose interest in the game and it dies.

Absolutely. However, all the other players have this right too and where your rights and their rights are in conflict, that conflict has to be resolved. "My way or the highway" is a method of dispute resolution - it is unlikely to be an optimal method.

How to fix it

Apologize - always a good first step in making things better. Even if you disagree with everything I say and maintain that your position was 100% correct and above reproach I am sure you are sorry about the way things turned out. You wouldn't be asking this question otherwise.

Reset and restart - decide if you want to (or can) go back to the status quo ante, or continue from here, or euthenise the campaign.

Discuss - listen to their arguments and understand their position. Explain yours. Make arguments that will change people's minds, not ones that entrench their opinions against you. Know what your power and influence in the group actually are, not what you think they are.

Resolve - make a group decision that the group can live with even if individual members (including you) are not totally happy with.

Learn - always learn.