I'd be fine with either a tucked or laid-out flyaway. She can already do a tucked flyaway fine from a tap swing (though she's still a bit nervous about it).
Generally, I prefer to teach layout flyaways first, and not even teach a tucked flyaway until the gymnast is training double-backs. To me, a layout flyaway is simpler -- it's just a tap swing and a release. But this assumes a gymnast small enough for me to spot through a layout.
Okay, here's what I'd do. I use this method of spotting for all the kids to teach the flyaway since someone showed me it, as a relatively small female, some of them are the same size as me. however I haven't done it with anyone actually bigger than me. But I get what you mean about not being able to "carry" her like the release to candle carry. I myself could only do that with the really small ones. But this is almost as good, however the downfall is you will probably need to do it on a lower bar than she can swing through with straight legs so she'll have a do a bent leg swing. Smaller kids will be able to do straight leg swings.
What you do is stand facing the kid slightly to the side with your good shoulder towards them. You're going to end up resting the kid's weight on your shoulder. Basically they're going to hold the bar as they would before releasing for the flyaway, with you holding them so their lower back rests on your shoulder, and if it's your right shoulder then your left hand will be on their near side and your right on their far side. Then they let go and you move back a little as you flip/roll them down in front of you, still holding their hips/torso. it's very controlled. Then you can have them do swings to rest on your shoulder, making sure they do a correct toes up, open shoulder position ready for the release. Then they do swings and you catch them in the position, and flip down. At this point they can do layout. You can also start doing it without the shoulder rest but still facing them and flipping them down in front of you holding the torso. However just get used to the shoulder action first and have them used to it. it's very easy to displace them from the bar using this method.
For this girl once she's comfortable with doing it from a few swings, I'd have her cast into it. Cast toes down (make sure she doesn't bend the knees too early) and bent when she needs to (in order for you to catch her on your shoulder in the correct position the bar will probably need to be somewhat low. I just do it on the low bar of a bar set). Then catch her on your shoulder in the release point, etc.
Hopefully that makes sense, I don't have a video unfortunately. Again this isn't exactly ideal because it needs the bent knee swing, but it is very easy to spot without having to hand carry the kid but having a high degree of control.
There's also this drill
Though I've never tried it: YouTube - gymnastics - introducing "flyaway" dismount
YouTube - Flipping for Flyaways - Tony Retrosi
(a little more explanation in that one)
A drill idea for displacement here:
YouTube - Fly away drill
And this one, which I like, but it's hard to set up, and if she won't do the release now it just may not be for her. What you might do is set up less of a harsh angle and then try. Maybe as last resort: YouTube - gymnastics - introducing "flyaway"