Good advice. I like the incremental progression and alternating over and underhand long toss idea. We just started the long toss walking in, which turns into running in. lol. We can only get into a large facility this time of year once a week, so it maybe one week over and one week underhand, which probably is ideal for her age.Presumably she is not going to be P only at 10U (or 12U or 14U). She'll need to work on her overhand throwing to play other positions on the field, as she should. Perhaps you could consider throwing overhand long toss one day a week and underhand long toss a separate day during the week. Long toss is easy to overdo (thinking about younger girls), especially if they are competitive. My suggestion would be to warm up, progressively go back in roughly 10' increments until she gets to the end of her range. Give her 3-5 throws at the end of her range and then have her start walking back in in similar 10' increments. Would recommend walking/running into the throw to help generate energy.
Once she physically matures, I think you can do underhand long toss more frequently. For my DD (15U), we try to incorporate some underhand long toss into every outdoors pitching session we have. We follow a similar model to the above and once we are done (say about 10-15 minutes), move into our regular bullpen.
Anecdotally, I have seen overhand and underhand throwing speed correlate pretty closely.