I haven’t done user support for Beeminder for quite some time so take this with a grain of salt, and it’s definitely not any sort of official comment!
It sounds like a way to take up support time that could otherwise be avoided. :-/ If it’s predictable that you’ll sometimes fail to meet the goal for those reasons, then the early deadline doesn’t sound suitable for this goal.
If I were doing this for myself, I’d have two goals. One would require maybe 4 or 4.5 hours per day with an early deadline, and the other would have the remaining time with a late deadline. It would force me to do the bulk of the work early, but give more leeway for the rest to account for appointments and sleep issues.
(At least that’s the simple version. What I’d probably do is have just one goal with a late deadline that I’d enter all the data into, and then a technological solution for populating a second goal with an early deadline with some or all of that data, probably with a setting that prevented any safety buffer being built up on the second goal.)