I’m inclined towards something like what Alys is suggesting, myself. I think that if the early deadline is something you’ll predictably have to miss, then I’d have the main goal with a late enough deadline that getting it done will always mean getting it done on time according to that deadline. Then I’d probably have a basic +1 goal that has an “OR” in the success conditions. (I’m really getting into these disjunctive success conditions, actually; let’s see if that sticks.) The second goal would be “Finished Goal_1 on time OR had a meeting OR derailed Goal_1”, for instance. That would be the one that keeps me on track time-wise, and the other would be the main one that collects the data. (That "OR derailed Goal_"1 part is to make sure that you don’t pay twice for derailing the same in-the-world goal.)
This way, your derailments aren’t exceptions (which can proliferate like nobody’s business when you have to decide about them on the spot); they’re pre-planed plan Bs that you can predict and set up contingencies for. The in-the-world goal itself can flexibly meet expected real-world contingencies, and the Beeminder goals can still be very bright-line-y.
I think that’s the general shape of the kind of thing I’d try for this.