I don't think turning off stabilization will speed up your focus for BIF...most likely, your problem is all in the lens' gearing. The solutions are pretty much universal, regardless of which brand camera you are using - better lens, hypersonic focusing motor in lens, better gearing, lens with focus limiter, more money! Buying the el-cheapo big zooms won't help you with Canon either - if anything, you have a disadvantage since you can't get stabilization. You're just seeing the basic limitations of a lower cost lens that can do a great job optically, but suffers a few compromises in areas such as focus speed.
I'm not sure how practiced you are with birds-in-flight shots, but you can still score some lovely shots just honing your technique and working around the lens' limitations. First off, accept that this type of shooting will result in quite a few misses...even very good bird-in-flight shooters I know with cracking good fast primes on full-frame bodies and top tracking AF systems will throw out 8 or 9 of every 10 shots - it's the nature of the game. Second, you might try manual focus (crazy as it sounds, it's not all that hard - and if you pre-focus a particular spot where the birds are flying, you only need small tweaks of focus especially with a smaller aperture...it'll prevent all the hunting around the lens will do trying to AF). Or, use the pre-focus technique with autofocus - find a tree, patch of ground, anything that is around the same focal length you expect the birds to be - focus on it, then when the bird comes along and you get it in the viewfinder, the lens won't have to crank the focus as far to achieve focus...avoiding spinning the lens from one end of the focus to the other while the bird flies out of frame. When shooting birds, I find using AF-S mode is often best and more accurate - track bird, half-press for confirmation, fire...no AF adjustments during the shot. And I typically use spot meter for cluttered backgrounds or larger birds. And if you haven't already, when shooting birds against a fairly empty background (such as sky), consider setting your camera to Wide focus area, AF-C mode - two different settings for two different types of bird in flight shots. The AF-C mode will tend to track nicely, using the full AF grid as needed, when there's nothing in the background to pull the focus away - so birds in the sky are fairly easy to let the system track for you and just fire frames.