Best lens for high school tennis

Hi,

I'm having trouble deciding the best lens for shooting my daughters tennis matches. Am considering the 100-400L IS. Also considering the 70-300 is. I like the idea of the extra reach of the 1-4. I don't think the extra weight will bother because I'm basically sitting for hours. I've read that the AF is much faster with the 1-4 than the 70-300, which would be useful for outdoor sports. I have also considered the 70-200 f/4 IS, possibly using the 1.4 tc. Would also like to use the long lens for wildlife. Any insights would be appreciated. Many thanks.

Current lens lineup includes:
Canon 24-70 2.8 L
Canon 35mm 1.4L
Canon 50mm 1.4
Canon 100mm 2.8 macro.
Canon 135 mm F2
Canon 1.4 TC