What is the best free tool for a complete SEO audit of a website of more than 1,000 pages?
Not sure which would be the "best." That can be a bit subjective. Wordtracker has a good one. They have been in the SEO business for a very long time.
Seobility is a free SEO audit tool that crawls up to 1000 pages with the free basic subscription. The tool provides a full-rounded analysis for your website, identifying SEO issues your website has.