My advice? Skip the synchro. It's expensive, with no ways to cut costs (other than fundraising), and it's something she can always do later if she develops strong skating skills now. Lots of colleges have teams and if she's still interested she can do it then - it's a great way to make friends, stay involved in skating, represent your school, and be a part of a team. If she puts the work in on her skating skills now, she'll have a lot better chance of making a team in the future than if she does synchro now but has to skimp on the rest of skating because of the expense of synchro.
Yes, skating is incredibly expensive. But it's also incredibly wonderful and has been a truly irreplaceable part of my life. I learned more on the ice than anywhere else, and I use the (life) skills I learned in skating every day, even if I'm not competing or training anymore. At the end of the day, it was never the glamor of the glitter that were why I loved it (though those things are nice); it was the indescribable and uniquely wonderful way it made me feel. I still haven't found anything quite like it. So if she really loves it, let her skate, if you can.
A few years ago, Braden Overett wrote a piece about his process of retiring. I think he did a great job of expressing some of the invaluable things one can learn from skating:
While everyone's experience is different, the characteristics we each share are the real assets to growing up as a competitive skater. Just to survive in the sport, we've had to work through days that seemed impossible. We've had to communicate one-on-one with adults. We've learned the meaning of hard work and dedication, and suffered from lackluster efforts. We understand why to pay meticulous attention to detail, and how much small mistakes can matter. We've experienced both the benefits and the pitfalls of being the center of attention. We know how to set goals, push boundaries, manage our attitudes, and follow through on commitments. We have a sense of independence and are capable of making ourselves grow... as students, as employees, and as people.