I was going to suggest the stroke-based method.
e.g. every 100ms (and on mouse up/down) capture the line-segment.
Capture the whole set of segments, then process it.
Merge lines, one at a time, and maintain a priority queue based on the "best-match rank"
You need to merge the most similar two lines each iteration to guarantee the best result.
You need a heuristic to rank how similar the current set of line segments is to your ideal line segments.
I think you can't just ignore magnitude, I think you need to use relative magnitude to the whole shape (e.g. normalize it).
Then measure the angle from the previous stroke.
Use the sum of least squares to rank it?
Repeat until you merge everything into 1 line.
The top ranking match on the the priority queue is your current best answer.