Sorry about not getting to this earlier but my ISP is having real problems today. I get on and then I'm off. Not sure how long this will last.
Mox,
I'm a surveyor (its one of my jobs) and know a bit about its history. The following was the general procedure used by the original surveyors of the public lands in the US.
After the lands had finally been ripped off from the Indians (OK, I just had to get some type of political jab in here) two teams of three surveyors was sent into the new lands. They would designate a point of beginning (usually trying to make that at a convenient intersection of latitude and longitude and near the center of the southern portion of the state) and then start the process of laying out the townships. They would usually start by going 6 miles north, then 6 miles west, then 6 miles south then 6 miles east back to the point of beginning. At each corner they would pile up a bunch of rocks or use whatever they had to mark the corner. Once the township was done another team of surveyors would come in to lay out the Sections (and they generally worked the same way).
If you follow me so far, you can see that a team could easily do 2 to 4 townships from the first point of beginning (but this would be a rare case as all of the teams I've studied so far worked from south to north). So eventually the team would have to pack up and go to one of their previous corners and start again.
As far as I've studied, there was no directive from Washington about which way to go once the surveyors arrived at a given location. This was usually determined by the team themselves and would depend on how they felt that day, how difficult the terrain was they were going to have to cover and if there were any hostiles in the area (many survey teams were killed and others had to be guarded by federal troops).
For a more graphical representation, if you are familiar with either the states of Ohio or Wisconsin (the two states I've studied the most), the surveyors there started at the south end of each and then worked their way east (one team) and west (another team) laying out the first set of townships, then gradually worked their ways north.
To answer your specific question:
"it is serpentine for practical as opposed to mathemantical reasons.",
you are partially correct in that the townships at the southern borders were laid out first (east to west and then north to south). But to follow the logic, wouldn't the number 1 be in the bottom right corner?
Here are a couple of sites that may make more sense than I:
http://geology.isu.edu/geostac/Field_Exercise/topomaps/plss.htm
http://www.geography.wisc.edu/sco/plss/index.php
http://www.dnr.state.wi.us/org/land/forestry/Private/PLSSTut/plsstut1.htm
I hope that makes things a bit clearer.