I'm an autocrosser with experience setting up, maintaining, and troubleshooting both an older T&S system, and the new system used by the SCCA at national events. Ours was the first local region to install the new "national" system, so I'm familiar with the "issues" surrounding the current T&S options.
There are several practical issues with optical systems for automated vehicle recognition- number and class markings are already tough to get consistent without requiring an additional barcode or QR large enough (some competitors would gripe about a huge barcode) to be useful at the 30'+ distance finish line sensors are set back to minimize getting hit by spinning cars. Add in the fact that existing markings some times fall off on course, or competitors in dual driver cars forget to change numbers between runs, and it's tough to be certain you'd have something consistent to try to recognize.
The national T&S system uses a wireless barcode reader operated by a worker in the starting queue to read stickers placed on competitors helmets to register cars in the T&S software. Locally, we position the T&S trailer to allow the operators to manually enter vehicles as they enter the start queue. Human eyes really are the most flexible here "shouldn't 80ES be 180ES?".
I like one of the comments above about a webcam triggered by the finish light taking a picture with a clock display in it. Unless there was OCR to immediately post the result to the software, the results feedback would be too slow for our region- we have real time announcement of finish stats, and the software can post results to a web server real time for smartphone access in paddock. The T&S software uploads a small file to the web server in the 20ish second gap between finishing cars.
Apologies for not offering solutions, but hopefully the extra info about some of the issues can help shape a solution.