I can immediately see 18 generations; that's just looking at 1 horse in the 9th generation. You might want to still use the Del Mar as a baseline for your research. Get print-outs, or whatever is most convenient, to lay out before you the vast pedigrees.
Also, if they're not already shown on DM, you can check the old-pedigree TB websites, like (TB Heritage) http://www.tbheritage.com/ and (TB Bloodlines) http://www.bloodlines.net/TB/ (my favorite). I know you probably already have used these, but just in case, I'm hi-liting them.