The 30D will only AF if the max aperture of the lens (or lens and tc combo) is f5.6 or wider, a 1.4x tc will cost you one stop while a 2x will cost 2 stops. So your 300 f4 used with a 1.4x will become a 420 f5.6 and still AF fine and with a 2x it becomes a 600 f8 so you'll lose AF. The Sigma 70-200 being and f2.8 should AF fine with either a 1.4x or 2x tc (becoming 98-280 f4 with the 1.4x and a 140-400 f5.6 with a 2x).
I had a Sigma 70-200 f2.8 for a while and did use it with a 2x tc (I think on a 350D or 400D at the time) it retained AF however there was noticable slowing in AF speed so it wouldn't be ideal for motorsport. What brand of TC have you tried on your lenses, I wonder if this is causing the problems?
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