What to do?

I'd shoot for Aerial Ace since you seem to be covered on Dragon type attackers. Rayquaza is significantly better than the next best Flying-type. If you change your mind, yoiu can always TM out of it

I don't know, friend. Maybe down the road, when there are important Pokemon weak to Fighting (and if Dragon Ascent is ever a thing), an all-Flying Rayquaza will come in handy. But right now, there's just not much for it to do (no relevant Bug, Fighting, or Grass types out there right now; OK, Machamp, but who's not ten-deep in that yet?).

When I plugged in my Rayquaza into Pokebattler as all-Dragon and all-Flying and ran the Attackers ranking, I got the following results:

Flying: Overall (didn't rank), Time to Win (didn't rank)
Dragon: Overall (#6), Time to Win (#4)

I'm bored with the Dragon Tail/Outrage set, too, but right now I don't think Ray's really worth sinking resources into as a Flying fighter. But if the variety is important to you (and it has been for me as well), go for it. It will at least be a different game play experience to have.

Otherwise, the Dragon moves will continue to be handy versus the awesome Dragons to come. I'm going to use mine as part of my growing unique six-Dragon team (no duplicates).

Dragon:
If Latias/Latios become Raid Bosses, Dragon would have a higher use + it's a stronger generalist moveset (the strongest afaik). Even in future Generations Dragon will be useful, since there will be several Dragon Legendarys in them

Flying:
He would be the best flying attacker by far, but his flying moves are garbage and his only use would be Machamp unless they shake up Raids. Afaik his Dragon moves would have a higher utility in upcoming legendary Raids (across generations). Flying moves would also make him a worse generalist

What do I recommend? Dragon.
What would I do? 1 CTM, done.

That's my choice.

if TM are not a problem, why don't you just switch moveset according to your needs of the moment?
if now you're in urge to use the best flying, change in that way.
when you will need a squad of strong dragons, change again.

with TM you can have the peculiar moveset you need, when you need it. Just a matter of time (to stock TMs)

For now only use for a flying moveset is Machamp raids. For bug and grass moltres is the way to go. Six lv20 ray can solo champ already. We have lati raids not so far ahead.