Personal opinion follows and i'm no authority.

"I multitask. And when I multitask, I tend to divide my attention,
wander through projects, look up something on the Internet, etc etc
etc."

You've identified that you don't multitask, you distract yourself.
Solution: manufacture a methodology by which you cannot distract
yourself -
there is only one piece of paper on your desk.

However, you currently appear to have a system that means as soon as
you raise your eyeline 3 inches you will see a mass of work.

Not good.

The other work you have around you should be available, but not seen.
By having it visible, it will trigger you to think about it, beg you to
work on it.
If this is how you wish to work things, so be it, i would contend
though that your system should encourage you to think about something
when it is most advantageous to do so.

Avoid the mental rabbit warrens.

Your system seems to decrease one of my key goals in "GTD", Velocity.
Do one thing at a time, but do that -very- fast.
Remove all waste activities around your execution of that task.

You've found that yourself, turn off the monitor - narrow the pipeline,
focus your mental push on one thing and fly it through that pipe. Your
piles of paper will probably become your new "monitor" that you have to
turn off.

"In practice, I actually like having my projects in front of me.
There's something tangible about it that's extremely helpful."

Ask yourself the "5 Whys" as to what possible benefit there is to
having a lot of projects on your desk that -you can do nothing about
right now-. (unless you wish to distract yourself from the task that
you were doing.