So, this took a while but I finally have some more concrete results on the speed trap synchronization.
The data shown is from this year's Hungary race.
To smooth out the speed trace and for better interpolation results I am fitting a 3rd order polynomial over a 5-second window of data. Through some trial and error this has proven to give the best result.
There are two metrics I use to evaluate the accuracy of the result.
The first is the variance of the finish line position.
The second is what I call "lap time integrity". The lap times are of course know very accurately. The time between the beginning of two subsequent laps should in theory be exactly the lap time. But this is not the case because of some inaccuracies when calculating the time. The difference between the correct lap duration and the calculated lap duration is what is shown in the second comparison.
All comparisons are shown as histograms to easily visualize the distribution of values. (Note that the width of the bins is not exactly the same, but it's close enough to compare the result)
A few things can be observed:
1. The speed trap sync is less accurate. Both distributions are wider than when using the current sync implementation.
2. The average finish line position is about 20-30m earlier in the lap when synchronizing based on the finish line. Which one is more correct is difficult to say. I don't think a 30m error to the actual position would be too much of a problem as long as it is a constant error for all laps.
3. The small extra heap at -1250 in the "X Pos hist orig" are in and out laps.
Conclusion: Synchronizing based on the finish line speed trap is not better than the current way.
Additionally, 5-10m of position variance and about 0.05s of lap time length error are not that bad really. It, of course, means that we can't look at a graph and say "driver ABC is breaking 10m later than some other driver into this corner". I'd really like it if we were able to get the accuracy down to that level but I am starting to doubt it.