AE is for working on shots not movies. Typical comp length for most projects that involve moving images made with a camera is usually ten seconds or less. Most AE comps do not involve more than on shot because AE is for compositing and motion graphics, not for editing. It is the wrong tool.
You don't gain anything in your production process by previewing at 60fps or full resolution if the Comp Panel has a magnification factor of less than 100%. In most cases you'll get a more cinematic look if you produce your film at 24 or even 30 fps. To see what the comp looks like, especially at 60 fps you can set the preview panel to skip 1 or even 2 frames. You should also have your comp panel resolution set to auto and have the magnification set to 25 or 50%.
There are no systems that I know of that would fit in a desktop machine that will preview 30 minutes of HD footage at 59.94 fps using any compositing or motion graphics app. It's just not possible because of the way compositing apps work. I don't know what you are planning to do with the Cars Main Footage but the best workflow would be to trim that footage to just the frames that are going to be used in the final production, then do your AE work. If the work you are going to do on the footage cannot be done in a non linear editor, and you have to process all 30 minutes of footage then I would still break the shot down into comps that are about a minute long and then stitch the project back together in a NLE.
I also don't know why you are using a proxy. Rendering an H.264 proxy will KILL your effects processing speed because the CPU will have to decode the footage, figure out what pixels go in the imaginary in between frames you get with MPEG compression, amplify compression artifacts and noise, and give you a final product that is significantly lower in quality than the original. It takes about 1/4 the time to decode lossless formats. Image sequences decode even faster. The standard use of a Proxy is so you can preview motion and timing at a lower resolution and get the "pencil test" portion of your project done in less time. A pencil test is where you preview animation without all of the effects turned on so you can adjust the timing. The term comes from cell animations that used simple sketches to lay block out their shots before ink and paint finished the shots. Once you have the timing and animation working you the original footage is brought back into the project for final visual checks and rendering. I can think of no possible other use for a proxy. From what I gather about your workflow you have set up a loose loose proposition.
I hope these suggestions help. It would do you good to study industry standard workflows and figure out what will serve you best. Just poking around in the app and inventing your own workflow because you heard somebody say something or watched some YouTube tutorial by an amateur is usually a huge waste of time.