A couple of observations - 1) heading up from the north with more than 1 liter of fluid is excess weight. Superhydrate before you start, and then tank up at Madison hut. 2) The Watson Path is interesting, but it's steep, rough, and slower. To illustrate - when Brutus was about 3, he accompanied a group of us on a Presie traverse starting up Valley Way. They split off at Watson, while he and I continued up Valley Way. We visited for about 15 minutes at the hut with a gal very interested in Brutus, and then on to the summit. My friends, who were faster hikers, didn't arrive until 10 minutes later - rather tired and a bit fried. The take away is familiar - the shortest route is not necessarily the fastest. I've found the same is true if you start the traverse via the Pine Link - by the time you struggle to the summit of Madison, Pierce seems a helluva long way off!
Since this is your first traverse, I'd go with the conventional wisdom - go north to south, travel light, know your water sources and how much to carry between them, go up Valley Way, and avoid Clay, Jackson & Webster. Get creative on subsequent traverses. Avoid making your first an epic.
YMMV.