Do the biggest. Do the hardest. Do the one that will make the most progress.
Even if you can only get part of it done. Just start.
Do it first thing in the morning, with no distractions for 90 minutes and see how much you can get done.
Do the top priority then move onto the second for 45 minutes. The move onto the third for 45 mins. Do all these things before checking email. Turn off your phone and Skype. Obviously turn off your email, but it already will be turned off, won't it?
Shortcut to productivity: Proactive in the morning. Reactive in the afternoon. I have not read makers schedule managers schedule but the principal sounds similar.
You cannot get much actual work done in tiny chunks. Do not let other peoples meetings whittle your time down into bite-sized bits. And don't let them go over your most productive time - usually the morning.
In the morning you can usually go for 90 minutes without a break. In the afternoon only 45. Schedule accordingly.
Once you have done work on your top 3 priorities (or it may just be the top 1 depending on the day) then forget the rest. You are done for the day.
Most people never get this much done in a whole day. Congratulate yourself that you have just done in 3 hours more than anyone else because you took the time to carve out some uninterrupted block of time big enough to actually do something meaningful. Most people scatter this time throughout the day - checking email. Making tea. Chatting. Getting overwhelmed with other peoples agendas.
Remember, just because it is important and urgent to them, does not mean it is automatically the same for you.
What if you were on holiday? What if you were off sick? What if it was the middle of the night because they are in a different time zone?
They will cope for 90 minutes. Look after yourself first.