A question about a specific lens for Canon

[tyler_h]

You would lose some f-stop using a tele-converter with the 70-300, and of course have degraded image quality.

I would just save up for something perhaps like a 100-400L.

This would be my suggestion. I didn't see it mentioned but I assume you're working with a crop body. 640 f/5.6 at the long end is long enough, and you'll need to stop down for DOF anyway so fastness shouldn't be an issue (hope you have a tripod/monopod though).