Bugger the tour. Easy peasy for you to get around by yourself and hit a few highlights. Big question: which 19 hours is it? Obviously if landing at 7 pm and leaving at 2 pm, your opportunities are lessened than if you land at 7 am and leave at 2 am.
The strategy is a good way to cram in an essentially free taste of Beijing. As you would not need a Chinese visa for under 24 hours. If you decide to change your ticket, give us the details and we can do a play-by-play of good options for you.