Admiralcapn, as others have stated, the portion between Jackson and Blackfoot will be basically impossible. From Blackfoot east/southward, only the ridge to Logan will present snowfield crossings that could be treacherous. The Norris Traverse itself (Red Eagle to Tri. Divide Pass on the divide) is doable in 2 days, but it takes a solid day to get to Red Eagle Pass from anywhere (2 years ago I did this route starting from Cut Bank, plus bagging all of the Little Chief to Red Eagle ridgewalk, all in 3 days out to St. Mary... last year I climbed Razoredge, completed half of the Norris Traverse out to Split Mt. and back out in one and a half days).
I agree with Ear Mountain's assessment of a 4-5 day trip if you do indeed have the skill and experience to do your entire trip. My advice: Just do the Norris Traverse. It is a great route and will likely take you 3 solid days to travel between Gunsight Pass TH and Cut Bank CG. Another option for doing the Norris Traverse would be to ascend to Almost-A-Dog Pass via the Virginia Creek drainage, but this area can turn into a god-awful bushwhack if you do not reach treeline on the western slopes of Citadel/Dusty Star to ascend to Almost-A-Dog Pass and the bushwhack to reach this treeline from Virginia Falls is also a hardy uphill bushwhack.
Another thought... if you simply want to do some long class 2/3 ridgewalking on the Continental Divide, there are plenty of similar routes in the Southern portion of the park that would be much easier than Mt. Jackson to Triple Divide Pass, such as Triple Divide Pass to any combination of Cut Bank, Pitamakin or Dawson Passes. Another route I have done along the divide that is similar is to access the Continental Divide from Bearhead Mt. via Mt. Ellsworth, all the way to either Firebrand or Marias Pass.