People are going to jump all over me for saying this, so I'll have to put in a disclaimer that says I don't recommend anyone follow my lead.
I take some new good-quality 400 grit sandpaper, wrap it around the rope, and VERY gently slide the rope through. A very light touch is all it takes. You can do the whole length of the rope in about a minute. The sandpaper is so sharp it cuts a few of the surface fibers, maybe 2% or so, enough to raise a light fuzz. That's what you're after. The rope comes out looking and acting about the same as if you had used it in the tree for a week.
Advantage: the whole rope is uniformly treated, and has uniformly improved friction properties.
Disadvantage: a few sharp particles of sandpaper may end up embedded in the rope.
If you look at any well-used rope, it will have LOTS of broken surface fibers and it will contain a significant amount of dirt, some of which will consist of sharp particles. I think my method is less harmful than letting someone break in your rope for you by actually using it out in the field for a week.