I´m facing the exact same problem right now! I find that my brain simply isn´t functional (as sleep deprived as it is) without frequent distractions. They could be LESS frequent, but they are definitely something that has to be done.
A trick that a friend of mine taught me was to do each thing for five minutes, setting a timer. At the end of five minutes, even if you are in the middle of writing a word, stop and switch to another activity (like reading discussions here) for five minutes. After that, move up to ten minutes, then 15, etc. If you have to stop and take a break, start again at five minutes. Knowing that you only have a few minutes to do something really gets you in the work mode.