Emerald circle sorcery can be used to perform adamant circle workings, albeit at greatly increased cost and difficulty.
Incorrect. A Sapphire Circle Sorceror can attempt Adamant Circle workings, but an Emerald Circle Sorceror cannot, ever.
This charm may have some problems, but it's pretty clearly intended to be balanced primarily by ST fiat. It's a lot less broken if you sharply reduce the range or even require it to use an extension cord to get around anti-scrying wards.
I would have included a clause to the Doombot Charm that allows someone to "see through it" PRE-actively.
Like, if another Solar uses Eye of the Unconquered Sun to determine if you are you or just a Doombot, you must either IMMEDIATELY spend the 30 white points to use Dual Magnus Prana, or you may absolutely NOT use Dual Magnus Prana until you can next re-establish surprise.
In essence, you can collapse the Schrodinger's Cat waveform of Doombot/Not with at least the one Charm in the game that should reveal the truth -- even to the point of reversing Lunar shapeshifting!
If Dual Magnus Prana is going to be the Solar equivalent to Duck Fate, it really should have ways to beat it just as Duck Fate does. Not necessarily the SAME ways, because of course they have very different justifications, but it should be possible to counter this.
And if Eye of the Unconquered Sun can't counter this, that needs Errata or Houserules.
EDIT: Eye of the Unconquerd Sun doesn't specify Lunars; it says it returns a shapeshifter to a natural form.
Time will tell if stolen forms count as natural enough for the Lunar Exalted to ignore this imposition entirely. If not, a Solar may expose a Lunar just to get a Tyrant Lizard or Deadly Beastman in his face for his trouble.