I'm probably going to have to rewrite some parts of this, because of how it's evolving. Which is good.
The Royal Moon Navy's ships were built primarily around having a sizeable corps of mages, with at least one capable (if not necessarily powerful) mage per ship. Obviously Apollo doesn't have this, since he isn't even a mage and is on his lonesome, so he's worked around the problem. He'd really like some mages though.
Senshi are extremely powerful mages due to their link to a planetary mana pool, and although not trained for operating a ship, would be a significant aid. Even Tux-boy, with a modicum of training, would be an asset. I'm viewing the Senshi status as being an office - when Beryl attacked, Queen Serenity's generation of Senshi were wiped out and their designated heirs (who would have been mages in their own right) were primed to take over automatically, subject to being activated (given the pens, basically). That was tied to the soul/magical core, which was reincarnated rather than the bodies which also died in the attack (or Serenity's mass reincarnation working, but without having heirs to pass on to, stayed with them. This had happened before in isolated cases and usually meant a gap in the succession for the affected Senshi until the reincarnate was old enough to be activated, and a dynastic scramble since while it was traditional to pass Senshi-ship down a family, reincarnation doesn't tie to a family.
The monarchy is not a magical working of the nature of being a Senshi and the Senshi are not part of the succession because they are senshi (although a blood relationship is possible, and in fact the case. For the purposes of the fic, in the Silver Millenium, Sailor Venus would have been fairly high up the succession, although her claim has the same bar as Usagi's). They are inherited by heirs of the body and reincarnation does not trump that. Usagi's claim to the throne is seen by Apollo in about the same way as I would be viewed if I walked into the parliament of Macedon and declared myself King by virtue of being the reincarnation of Alexander the Great: even if she can prove she is the reincarnation (possible, although Apollo can't do so himself) it doesn't make her claim legal...
Which doesn't mean that it might not be accepted. The situation is unprecedented after all.
Apollo curled up in his command chair and buried his face under his paws for a moment. "Computer, what are the laws of succession relevant here?" he mumbled.
"There are three hundred fourteen laws relating to succession to the Throne of the Moon Kingdom," the computer replied. "Do you wish to narrow the criteria of your request?"
"Yes!" the one-eyed Mau snapped before the computer could start reciting the laws vertabim. "Filter out those assuming living children of the deceased monarch."
"There are one hundred eighty-five laws relating to succession to the Throne of the Moon Kingdom under these circumstances. Do you wish to narrow the criteria of your request?"
"Filter out those assuming a declared line of succession."
"There are two laws relating to succession to the Crown of the Moon Kingdom under these circumstances. Do you wish to narrow the criteria of your request?"
"No," Apollo said. "From those laws, who decides who takes the throne?"
"The successor is to be nominated by the Senate of Nobles and requires approval by a sixty percent majority of the Chamber of Deliberators and confirmation of qualification by the Throne."
"Well that's just perfect," Apollo said out loud. "The Deliberators are all dead, and if they weren't they all would have met their maximum terms long ago. The Throne hasn't even spoken to anyone for ten eons as far as I know and the Senate... well, there are the Senshi, but four members isn't close to a quorum."
The computer, not aware of a question or a request, was silent.
"Is there an alternative?" he asked.
"If no successor is nominated by the senate within one standard year, a majority vote of the Council of Ministers may place nominations directly to the Throne."
Apollo brightened. "As Senior Fleet Marshal, I'm a member of the Council aren't I?"
"That is traditionally the case for the uniformed head of the armed forces," the computer confirmed. "Status unclear however, as Council members are appointed by the Crown."
"And Queen Serenity died before I got drafted to command," the Mau whined. "Dammit. What about the Regency?"
"Regents of the Moon Kingdom are specifically prohibited from nominating successors or from voting if applicable on nominations."
Apollo could swear in an impressive number of languages.