Why would she run third party when she could easily capture the GOP nomination?
That's simple.
Many of the 40% self-identified conservatives in the electorate are independents or Democrats.
At least half of THEM (more where I live) hate the GOP brand so much that having that nomination would be a deal-breaker.
Sarah Palin's fraction of the non-GOP conservative vote would be greatly increased if she runs as a non-Republican.