Cross Country
I think in terms of restrictions, Steve is right, the only restrictive diff is the number of people allowed in a single party.
Well, to state what is probably already apparent to you, in terms of SAR info, since you will be heading off-trail for significant stretches, having every bit of info as accurate as possible on your permit would be advisable in case of emergency. Therefore I would select cross-country so SAR personnel would know (with out too much mental footwork needed) to look for you in non-trailed areas first.
Visiting Whitney
As far as "visiting Whitney" that permit designation is only for people who aren't entering/exiting via the Portal and by extent the Whitney Zone.
Namely, that designation is primarily for people hiking CP to OV, or PCT hikers who will just tag Whitney's summit and return to Guitar Lake. Those hikers technically only pass into the WZ for a cumulative 0.25-0.5 miles of trail length.
So... If you wanted to start your trek from Cottonwood, Meysan Lakes, or Cleaver Col, you could theoretically use a permit as such without fear of repercussions.
