I just started with my website and did a crawl. Subsequently I've been seeding it with the best results form my previous crawls.

It's a directed search so it doesn't seem to need a particularly solid seed to get decent results.

So how long did it take to get to 17 million URLs?

Not OP, but if I was to do this, I'd start by downloading Wikipedia and all its external links and references, and crawling from there. You should eventually reach most of the publicly visible internet.

I feel a little embarrassed that I didn't think of something like that.

When I did some crawler experimenting in my younger years, I thought I was pretty clever using sites that would let you perform a random Google searches. I would just crawl all the pages from the results returned.

Your method would undoubtedly be more interesting I think. It would certainly lead to interesting performance problems quicker, I bet.