I built a free physics-based Carambole & Danish pin billiards simulator (runs in the browser)

The game/simulator Virtual Pool includes a carom mode. The physics is pretty realistic. You may want to compare shots between your simulator and VP.

One thing I noticed immediately in your diagram is that the paths of the balls appear to be straight. Balls do not travel in straight lines.

Several other carom simulators exist, with at least two of them posted about here.
Thanks, I will have a look at VP.

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