After about two months of some serious taste testing, I have to report my results.

Not only does a French Press make a better tasting cup of coffee than using a cone filter, but the taste is so much better that it makes the mess and extra clean up involved worth it.
There is an art to using a French Press, and rather than recreating the procedure from scratch, let me just point you in the right direction. Kaylee Wood at Acceptable Addiction has it all spelled out to the letter. You can read the instructions on her site here:
French Press Coffee – Acceptable Addiction.
One thing I have found, though … if you just can’t abide by the sediment that will inevitably hang in the coffee coming from a French Press, you can always run it through a cup-top coffee filter.
But a little bit of coffee mud doesn’t hurt anything, and in fact, actually adds to the flavor.
From this point on, when I do a coffee review here, if it’s at all possible I will use a French Press to make the coffee.
(For the record, I still think a single-serving cup-top coffee maker is the second best way to make coffee.)