I think we're maybe overthinking this. If we go low, we'll avoid encounters, or at least avoid dangerous encounters, so that's the route we'll probably use. Which will take 2 days and some change. Which would leave four days by the time we arrive at Castle Black. This trip is basically mandatory if we want to visit Aemon, and even if we skip Aemon we'll have to fly over it and then move far enough away from it to get out of the interdiction zone.
But four days is enough to diplomance the giants.
So the plan is roughly this, for efficiency:
1) Bring Mother back to life.
2) Spend time on the immediate reunion, answering questions, etc.
3) Overland route with phantom steeds.
4) Arrive at Castle Black. Spend a couple days there with family/copying texts from the library after securing good relations with LC Mormont.
5) Leave Dany with Aemon and Mother, take Richard to the Fist of the First Men to diplomance some giants during the last two days of our earmarked time in the North.
6) Return slightly ahead of schedule to SD leveraging copious use of party teleportation.
7) Bust open a fine vintage of wine, because things are going suspiciously well, and this may be the last chance we get to pat ourselves on the back for a while.