Welcome to the world of photographing large, curvy, mirrors, Snooks! As a sporting analogy, I don't play golf, but I'm told that it is very frustrating and yet people keep going back for more. The curves on the ends of body panels catch reflections that are not very noticable in the viewfinder when a lot is going on in real time. Plus, there may be lots of chrome.

The other posters have covered the options I think, but here are my thoughts.

Distractions in the background against the shy are easier to clone out than distractions next to the body and reflections are the hardest of all. You can use a narrow depth of filed to minimise the background distraction and help post processing but this will not help with reflections. As you have discovered, A CPL filter does not make a noticeable difference, although they are handy to minimise reflections in glass.

For the benefit of other members, I was present at this car show too and Snooks had a relatively short stay, based on the need to get to another location before losing the light. Early and late are the best times when the crowds are at a minimum, but the downside is some car owners will leave early. So unfortunately time and patience is the key. Also handy are sunblock, water, food and in my case, some stretching exercises before going. I specifically went to this show to take advantage of the late afternoon light and then later, soft dusk light.

Now that you know about the impact of reflections, aim to walk around the car and look through the viewfinder at as many angles as practicable. You will have to compromise on composition, incident light, backgrounds and reflections. After that, you will have to wait even longer while the onlookers move on. They will not realise you are waiting for them if they are in the background or at the side and reflected in the body panels. If I spot the "must have" car and I have the time, I will try to return to the same car several times to see if the surroundings situation has improved. I keep scanning the area to try to catch opportunities, subject to the size of the show. With practice, you will be able to spot some potential reflections before looking through the viewfinder, by looking around the area of the chosen car. Reflections are less noticeable on the sunny side of the car than the shaded side. I sometimes use a flash to light up the shaded side, but this doesn't suit every shot, requires some practice to get it right, and complicates colour temperature matching..

It is painfully hard on one's knees and back, but I like to get down extremely low so that more of the sky is reflected rather than the surroundings. I will admit that my tilt screen helps in these situations, as I don't have to actually lie on the ground, which is not practical at a show. Light poles will still show up, though. Of course, this results in extreme angles that may not be your intention or preference. I am aware that you don't personally like my extreme high angles, or "Dutch angle", for instance, which I use to control surroundings and reflections. Sometime you just want to capture the main features of the car from car waistline height or a little higher.

In post, one trick I use is only possible in a small number of photos. If another car is reflected and it's colour is not present in the subject car, I reduce the saturation of the reflected car's colour. This can even be done globally, rather than locally, by brush or mask if the photo suits. I may also locally reduce contrast of the reflection with a brush. I also de-saturate chromework and this will reduce distractions in a limited way. These steps are an alternative to cloning and brushing colour, although the techniques can be combined. Cloning and painting is tricky and time consuming to keep it realistic.

Hope this helps.