So I was thinking while I was out doing a chore, and I realized that there was a piece of information about Stone Oaths that you might like to know: it will include pulling out your dragonstone as part of the promise.
However, since you were going to need to get your stone out anyways to half-shift and fly Sypha away to avoid the wyvern, I didn't think to include it at first. However, since I believe in giving you as much information as Ryza would know, I figured I'd mention it in case it made anyone change their minds.
EDIT: More information:
How the Oath works:
The reason Stone Oaths are powerful is because it is felt by a manakete's dragon as well. Whereas most promises a heart-form makes are only bind to the dragon-self as much as they consent to be bound, a Stone Oath is instinctively felt by the dragon. Barring extremely unusual circumstances, a dragon will instantly move to fulfill any Stone Oath they feel compelled by. Whereas Dragon-Ryza would instinctively move to protect Artemis because Artemis is her BFF, she'd instinctively move to protect Sypha because she promised to.
On the heart's side, the oath is half magically binding, half culturally binding. While Ryza's mother taught her all promises are important, Stone Oaths are on another level. It's like walking into Mordor: breaking one is just Not Done. The magical compulsion is similar to the compulsion on the dragon, but lessened by the fact that heart-forms are meant for slower, more thoughtful actions. While Dragon-Ryza would instantly and unquestioningly move to protect Sypha, Heart-Ryza would feel a need and want to, but she'd have time to think about how best to do it.
All this being said, it's not an Unbreakable Vow: you don't instantly die if you break it. It's just psychologically difficult to go against it. It's also not a fey promise/devil's bargain, where exact wording is everything. So long as Ryza honestly feels like she is fulfilling the promise, she won't feel any guilt if someone else tries to use exact wording against her.
This goes both ways, of course: she can't hide behind technical truths and say she fulfilled it. If she promises to protect Sypha and get her home as soon as things are good between Legerius and Agrithe, she has to follow the spirit of that. If the Archduke makes patently unreasonable demands and then uses Mantrae's hesitation as an excuse to hold Sypha longer (not saying he would, just if he did.), Ryza would recognize that was unfair and feel compelled to break her out and take her home, just as she did for Artemis. She wouldn't be able to say "Oh, Archduke Letoro says it's okay so it must be okay!"
Mechanically, if you take the Stone Oath option, it is possible that you would run into situations where I wouldn't give options on whether or not you would do something, just how you would do it.
Making the Oath:
Ryza would need to get her stone out and say some special words in a sort of mini-ritual, tying the promise into her dragon's mind. This would be somewhat flashy: wings would be out, ears lengthened, lightning flickering. However, it would not be stabbing beams of lighting into the air saying "We are here! We are here!" to the Talons and anyone else looking.
Also, Ryza would be careful to phrase it in a way she honestly believes she can keep.
Why Ryza would make it in this case:
Ryza gets the feeling that what Mantrae's people want is a firm promise that they can trust and rely on. She unfortunately still has an incomplete understanding of human promises, and so she might figure "hey, let's go all out and hope my sincerity shines through!" or she might think "They specifically mentioned divinity, so let's give them what they want." Both are potentially reasonable lines of thought, you as voters are deciding which train of thought wins out.
Also, part of the Stone Oath does mention the Mother in a more formal sense.
Nothing really to say on the dragonstone, save that Ryza thinks it decently likely that Mantrae's people would want to watch the transformation anyways, and since she has to sit quietly for an hour, she's not sure she could really stop them. She might be able to convince them to give her privacy, though.
