Okay so to start with my explanation of disagreeing with this downgrade, the biggest issue to address is part of the OP here:
So I found some inconsistencies with this calc that needs to be addressed. To begin, this isn't a moon moving feat to begin with.
11:18 if you look closely you can see that it's actually just panning. There is no moon actually being moved or any reference to such an event.
The OP is ignoring context as to what Tsukuyomi does and is capable of, especially by saying "there's no reference to the event of the moon moving", when that is in fact wrong.
Tsukuyomi is a Unit that, in several iterations of it's appearance in battles in the series, has blatant dominion of the moon as celestial objects. This is first demonstrated by Godess of the Full Moon Tsukuyomi calling forth a moon almost instantly just after being brought forth.
(timestamp, incase it wasn't embedded, is 18:11).
This, of course, is also not the only time Tsukuyomi does this either.
A
very damning case of this happening happens in this later episode:
12:30 - 14:16 demonstrate this.
Please read everything in this upcoming explanation.
Misaki has a cardfight with an opponent, and in this particular battle, we outright see (at 12:59 to be exact) that the environment they battle in on Planet Cray is completely sunny out. Clearly showing that it's daytime during the time of their battle.
This context is important, because 13:14 demonstrates that Misaki already has Full Moon Tsukuyomi out into battle as her Vanguard (for those that don't know the context of the series, a Vanguard is a Unit the cardfighter possesses to battle with, so in other words, Misaki is already using Tsukuyomi to battle with). That means, Tsukuyomi is brought forth into battle
during the day time in this instance.
Then, at 13:45 when we see Tsukuyomi getting ready to attack her opponent, the moon appears and it becomes dark in the setting to clearly resemble night time. And then uses the moon as part of her attack at 13:54. This means, Tsukuyomi called forth a moon during battle here, and
actively does this.
Finally, at 14:14 onward, after Tsukuyomi's attack gets successfully blocked by the opponent, the setting changes back to daytime like it was before (shown when Misaki prepares to attack her opponent with her other Units).
This case here is a daming instance of her moving the moon forth by coming into a daytime setting, showcasing the moon and making it night when attacking, and then it goes back to day after her attack is finished. Which shows Tsukuyomi has clear dominion of the moon, actively does this, and very much supports the idea that she calls it forth.
Now, in the case of Cresent Tsukyomi's feat, I'll get that in a second. But first, I want to show another instance of Full Moon Tsukuyomi moving the moon. And it's in the very episode the OP linked for this thread.
(Timestamp, incase its not embedded, is 20:38)
What the OP happened to not show in his post here
Is that Misaki uses Full Moon Tsukuyomi and a moon appears behind her when getting ready to attack. Just like I showed above. And here, the moon is definitely shown to be moving. But don't take my word for it. The scans here, to ensure they aren't dodged or accidentally missed, will prove it for me.
https://cdn.**********.com/attachments/574596090788315196/890259015735574638/image0.png?fbclid=IwAR0_pQdJVmu-AxiZZLobxvWJ1YiovM7N8PvQteshPDZZh0VZK6XLhswijh8
https://cdn.**********.com/attachments/574596090788315196/890259019560808528/image0.png?fbclid=IwAR3YxFEdAWiESlZo2shlpDEdbu_bAyhx0gtOdWtIneSHdiLirOSeu4ctDhE
The moon's positioning between these 2 moments, from the time Tsukuyomi attacks and by the time she finishes attacking, is blatantly not the same. We literally see the moon
behind Tsukuyomi when she's going into her attack phase, and then it's shown to be
in front of her, and her opponent, moments later when she's attacked. And we already know that Tsukuyomi actively calls the moon forth as part of her attacks, as the above clip shows is the case.
Why would the moon, during this specific attack phase, just randomly be in completely different positions if she wasn't moving it? The interpretation that it isn't, in this context, doesn't make sense and requires more evidence from the opposition to suggest an interpretation different from what the entire scene in and of itself already gives to us, and other supporting feats. More could be given for her, but I don't think I need to under these circumstances.
Now to address Cresent Moon Tsukuyomi's feat.
Supporting evidence of this is the fact that she's stationary on the ground at 11:04 just prior to flying up in the air.
11:26 you can now see more panning with her in front of the moon before she attacks. The attack at 11:30 then show's she's attacking from up above.
To start off with, this isn't really much of a counter. Her flying up in the air is to signify that she isn't sitting still and is going to attack her opponent. That doesn't necessarily mean the moon isn't moving simultaneously to be included in her attack phase. However, this is just a minor thing I wanted to point out. There's better reasoning for why Cresent Moon would be moving it.
Simply put, Cresent Tsukuyomi and her capabilities are
literally no different than from Half Moon and Full Moon, with the only obvious difference being each form is stronger than the other. Outside of clear power difference, all 3 variants of Tsukuyomi do the exact same thing as each other, and effect the moon the same way when it appears during their attacks in battles they are used:
https://cdn.**********.com/attachments/574596090788315196/890278955951726672/image0.png?fbclid=IwAR2Xy3rd3MGvs4UyAPnZrkrnW2QurQvkMK9jf_pA0FemXVm0RwV8yxU8Jn0
https://cdn.**********.com/attachments/574596090788315196/890278927128477696/image0.png?fbclid=IwAR1cXzSfufkaSgqMTNyE4KfQj4RYe2r2r1C5DoSDStD3KmFvEZbTE3gMZ3Y
(And of course, the scan of Full Moon Tsukuyomi above)
The basic run down? Given what all 3 forms of Tsukuyomi are capable of in relation to each other, and their obvious similarities outside of strength differences, it should not be unreasonable to say Crescent Moon Tsukuyomi can move moons like her Full Moon form generally can.
There is also another case of moon moving that should be clear too. Not as blatantly so as I what I showed for Full Moon Tsukuyomi, but it should suffice in making the point. Here in this episode:
Pay attention to the timeframes I will give.
Now in this episode, Misaki has a cardfight against one of her friends.
At 11:41, we see the area of where they are battling on Planet Cray. There is no showing of a moon being in their vicinity.
13:42, Misaki is shown to be using Half Moon Tsukuyomi as the Vanguard Unit she's battling with. Now, why is this important?
Because at 14:23, Misaki rides onto Full Moon Tsukuyomi, and in this instance, the moon is out before Full Moon Tsukuyomi comes into battle.
So what would this mean? There was no moon present at the start of the cardfight, but Full Moon Tsukuyomi didn't call it forth here since it was present before Misaki called her forth. This would be a supporting feat for Half Moon Tsukuyomi being able to, again, effect the moon in the same manner (unless one wants to try gunning for this moon appearing out randomly for no reason).
Anyway, this is why im entirely against the downgrade on every level. The OP's headcanon stance of what Tsukuyomi does ignores the context of what she's been depicted to be capable of in the series across all 3 of her forms, using an argument that doesn't even necessarily mean the moon wouldn't be moving.