It seems that my experiment with spreading deadlines across the day was a good idea.
I had previously a major problem with (on bad days) postponing everything till 23:00 and trying in panic to fix everything in one hour. Which was failing in multiple ways.
Now on bad days I get a much more direct and earlier wakeup call, which makes Beeminder more useful to me.
I forgot twice that I did it and failed to enter data, but these derails were reverted by wonderful support.
(I remember related/similar threads, somehow I have not tried this for a long time - so this is my +1 to the entire idea. Maybe Beeminder should encourage customizing deadline time a bit more (show it in goal creation menu?).)