We have used Marshall Cavendish Discovering Math, which was the (unmodified) secondary math used in Singapore not too long ago. It is definitely intended for a classroom, so we've had to make our own mods, but have found it to be a good balance of problem solving and sufficient repetition for fluency. I highly recommend doing the Brainworks problems, for extensions. The lessons are very thoughtfully laid out to reinforce earlier skills while learning new concepts, which reduces the feeling of repetition often found in math texts. The Brainworks problems often contain derivations or previews of subsequent skills and concepts, so that I often hear DCs making connections across lessons.
Most lessons have four levels of problems. We typically do every other item, though sometimes all of the items in the top two (application and extension). If the skill or concept seems not solid, then we go back and work the remaining problems.
This is not an independent curriculum, unless your DD has a particular affinity for math, and the maturity to manage her own time.
We've liked it enough to go through all four levels (pre algebra, algebra I, geometry, trig, in integrated curriculum), plus the Discovering Additional Math text, which covers more or less pre calculus and the beginnings of single-variate calculus.
We've used just the student text, but for even more challenge, there are also workbooks, with more practice problems, which are generally not of the drill variety, and test bank books, which are quite challenging.
One of the other homeschooled kiddos I know well is very like your DD, and has used the curriculum very successfully.
