Just to update with this info for everyone's benefit - following some experimentation I've discovered the Handbrake settings required to correctly convert DVDs into a format that the A3 will play, on Tech Pack equipped cars at least, can't speak to cars without this option.
Fire up Handbrake and select the Regular -> Normal profile in the Presets list on the right. Now select your source via the drop-down at the top-left. Note that, if the DVD source is copy protected (most commercial ones are) then you'll need to decrypt it to your hard drive first or else use something like AnyDVD to strip the copy protection on the fly.
Handbrake should scan the disc and automatically select the main feature, but you can alter this via the Title drop-down.
Now, ensure the Container is set to MP4 File. In the tabs below, leave the Picture and Video Filters tabs at their default settings. In the Video tab, set the Video Codec to MPEG-4 (FFmpeg) and change setting below it to Constant Framerate. Change the Quality setting to Avg Bitrate and set this to 1500kbps. I couldn't get decent quality output using the Constant Quality setting. You may be able to squeeze the file size by reducing the bit rate but quality will start to suffer if you push it too far. I also enabled 2-Pass Encoding but you may want to skip this if you're in a hurry.
The Audio tab should default to AAC Dolby Pro Logic II mixdown and this is fine as it is. Don't try to embed DTS or AC3 in the file as it won't be supported and you'll get no audio. Leave the Samplerate and Bitrate at 48 and 160 respectively.
Finally, you may want to remove any settings from the Subtitles and Chapters tabs.
That's it - go. Encoding is pretty quick, running at about three minutes per hour of video per pass on my machine, a 4Ghz i7. The resulting file should have an MP4 extension and will play fine in the A3 from an SD card.
Hope this helps some people out