Andrew,
Are you letting the camera select the AF point it uses? If you are, my advice would be to pick it yourself. I've no idea what camera you're using, but every DSLR I've used in the past has allowed me to do this and turn down the sensitivity a little to stop the camera immediately trying to refocus if my technique is a little sloppy and I let the AF point selected drift off target or something passes between the camera and target.
After that, it's all down to technique and holding the AF point on an area of high contrast on your target.
For race cars coming straight at you close up at speed with a long lens, single shot AF rarely works as the DoF is usually too thin resulting in one looks like back focus. Having said that, here's an example when it worked, but note there's a lot of right to left movement relative to the camera that helps make it work.
The massive advantage CSC cameras have over conventional DSLRs, particularly CSCs with EVFs and focus peaking, is ease of manual focus. On my G6 I can pre focus using a 10x magnified view with focus peaking, and then when I take the shot at normal viewfinder magnification, the focus peaking give me a blue outline around the high contrast parts of the vehicle as it passes through the focal plane. Much, much easier than using a conventional optical viewfinder.
The legacy lens are also much cheaper, and in many cases as good as their modern day equivalents. Ok they don't have any of the modern coatings so CA can be present wide open, but LR usually deals with that very easily. Put it this way, my pristine Tokina 300mm f2.8 and Canon 100mm f2.8, 135mm f2.0 and 200mm f2.8 in Canon FD mount cost me less than £750. Most of them look like brand new lenses. Of course with the right adaptor, these lenses will work on any CSC you care to mention (all manual of course) so I can change from for example m4/3 to Fuji X or Sony NEX mount and still use the same lenses.
I've just picked up a GX7, and the improvement in EVF and focus peaking sensitivity / control means I think I may be able to dispense with the magnified view when focusing which will speed things up.
This works for me, but certainly won't work for everyone. I just like the look, feel and handling of the older lenses and above all else have a huge amount of fun using them. At the end of the day, that's what it's all about
Cheers,
Simon.