those ideas aren't very similar, I'm definitely not confusing them with each other
Procrastination may have more than one cause. Like, if you don't want your china teacup to shatter, you have to stop it from falling on the floor, but you also have to stop things from falling on top of it. Both would cause it to shatter.
Sorry, that comment did not come out correctly. My bad. What I meant is that you might not have the right reason that explains why moving deadlines closer reduces procrastination.
I don't think anchoring is related to procrastination. Making the deadline closer may help procrastination, but it does not seem like anchoring is the mechanism by which it happens.
The phenomenon of anchoring seems to predict that deadlines will cause you to start a project near the deadline.
In more detail:
Any number you consider as an answer to a question will become an anchor and draw your answer towards it. Since you consider a deadline as a time to finish a project, your decision about when you should actually finish the project will be drawn towards it.
That'll make you start the project later, even though you know consciously that planning to finish a project near the deadline is a bad idea.
It's analogous to an example from Kahneman's Thinking, Fast and Slow—people buy more cans when there's a sign telling them that they can only buy 10.
So, what I'm predicting is that anything that prevents anchoring will reduce procrastination when there's a deadline. Consciously deciding when you plan to finish by adjusting from a much earlier time, maybe?
EDIT: Brendon_Wong points out that "procrastination" really refers to putting things off, which has an emotional cause. I think he's right. What I'm talking about isn't really a procrastination, then, but bad planning.