You don't need a company to help with logistics. Everything's easy to arrange. Jeep drivers will be waiting for you at Rakhiot Bridge to take you to Tato or Jhel. You have to use their Jeeps as they own the road. Porters can be easily hired in Jhel or Tato if you require them to get to Fairy Meadows. The walk to Fairy Meadows takes only a few hours. At Fairy Meadows you can easily arrange porters to Rhakiot BC which is an easy day's walk. Arrange things locally so that you put into the local economy rather than the Islamabad economy!
So far as climbing goes, the obvious 5000m peak is Bulder Peak (5600m) which is relatively straight-forward. It's about a 3 day round trip from the Rakhiot BC. I've not climbed it but the route looks straight-forward besides being on glacier. South Jalipur Peak (5200m) above Beyal is the other option. Very easy but views are probably just as good. No easy 6000m peaks in the area.
Bulder Peak from Fairy Meadows: