What is the most effective and least invasive way of whitening a root canal tooth?

Unfortunately your
tooth is no longer alive and is not going to respond to whitening the same way
other teeth. The best option is to try internal bleaching to lighten the tooth
from the inside-out (non-vital teeth almost always darken.) The standard of
care to protect long-term function and strength to non-vital root canal teeth
is to place a crown over the tooth. A crown will protect enamel from
chipping/breaking/further discoloration and give you the color you want.

You could have the tooth bleached both internally and externally.  The standard process for external bleaching is either Zoom or tray bleaching.  Problem is, if you bleach more than the one dark tooth, every tooth will get lighter, and the dark tooth (although still lighter as well) will remain darker than the other teeth.  Thus, would suggest just externally bleaching the one dark tooth.Adding internal bleaching to the root canal tooth, the dentist removes the filling from the back side of the tooth, and places bleach into the filling.  You might have to do this several times, usually a week or two between appointments when the internal bleach is changes.Saying all of this, it is likely that the root canal tooth will be lighter, but probably NOT match your other teeth.The most predictable approach is to do a porcelain veneer.  The dental ceramist and dentist can make the veneer much closer in color to your other natural teeth than you would probably get with the internal/external bleaching procedures on the root canaled tooth.

There is a procedure called "internal tooth whitening" or "walking bleach". It's done by placing a very concentrated whitening agent inside the tooth and sealing it with temporary filling. Tooth is checked weekly after that for the desired whiteness and fresh whitening material may have to be placed into your tooth. This procedure can be augmented with a conventional whitening of other teeth. After whitening is done tooth is restored with a composite filling. 

Normally a tooth that has had a root canal can be "internally bleached" by placing bleaching agent inside the tooth and leaving it for a day or two.  Repeated applications may be required to achieve the color you desire.  If there is any thing internally in the tooth like metal that is causing discolor then that would need to be replaced as well.

I would try external bleaching by your dentist first.  If this works you are done.  If not, then controlled internal bleaching in the office of short duration would be the next step so that you do not over whiten the tooth.