You don't want to string it overnight. That'll compress the belly beyond repair. This can happen easily with a sinew-backed bow. But yes, start with the long string on a tillering rig and work it in very slowly. When you've got about 7-9 inches of tip movement with good tiller still in tact at 50-75 pulls, move to a short string at a low brace height. Work the bow some more (again, 50-75 times), stopping about 3-4 inches of the bow's intended draw length (unless yours is shorter). Then raise the brace height to normal and work it in to the intended draw length.
You really don't want to spend more time than necessary on the long string, as it can give you a false reading and work the limbs slightly differently than the short string. Also, take it SLOW! When exercising the limbs, don't go crazy fast, as you can build up internal friction that can lead to limb failure. Let the bow relax back to its static strung position (whether short or long string) after each pull. And if the tiller looks off at any point, do NOT draw the bow any further. That'll need corrected.
Post lots of pics, and do add this thread to the Bowyer's Bench. There's a bunch of us that would love to help you out over there that don't spend a lot of time on the PowWow.