Go on some long (50mi+) rides, maybe even a weekend tour! You'll figure out what you need most quick enough. As you're already thinking about, the contact points (saddle, pedals, bars) are a good place to start. Consider clothes and other accessories too, if you don't already have them. I bring a few pairs of good padded shorts, jerseys and base layers, and a good hardshell rain jacket when I go on tour.
PowerGrips are nice, I recently did an 800 mile tour with them. Keep in mind they work best with a shoe that has a stiff platform. The trekking bars are also good. You can use your existing brakes and shifters, unlike trying to swap in drop bars where you'd pay a fortune swapping out components. You will need bar tape. Search Google Images for some examples. Bar ends are also a good, cheap way to add another hand position.
I would keep your disc brakes, other than the weight they should be fine. Lots of tourers would love to have them. I know I missed the disc brakes on my old MTB commuter the first time I took my new Long Haul Trucker with the stock brake pads out in the rain! A little rubbing is normal, but you might be able to improve it by making sure the wheel is centered in the dropouts and adjusting them a little bit. I'd also wait to buy new tires, as long as your current ones have life left in them.
Make sure you have everything you need for camping, buying a stove and all the miscellaneous gear you'll need can get expensive. Even things like sun block, bug spray, and medical supplies can add up quick. I have a Henessey Hammock too, and I know what you mean about it getting cold. Instead of buying a new sleeping bag you can consider a sleeping pad to help keep the heat in, or a sleeping bag liner. Wool undergarmets will help a lot too.