Hunza and Khunjrab are a piece of cake for any car. No issues at all.
Shogran road is narrow and pretty steep. Some cars, particularly automatic ones, can have issues. However, for Land Cruiser it shouldn't be a problem.
Road to Naltar valley, however, is in a different league. It can't be compared to roads of Shogran or Hunza. Parts of the road are as rough as Saiful malook lake road or track to Paye. Land Cruiser would get there, but I wouldn't recommend putting your personal vehicle through that. Hire 4x4 from Gilgit for trip to Naltar.