The traverse is definitely doable but more of an alpine route, like the Rundle Traverse, than a scramble. It took us 2 hours from Ha Ling to the Lawrence Grassi peak and 5 hours from goat creek parking back, but at a steady enough pace with no breaks and no mistakes in route finding, so give yourself longer. Trad gear/rope/harness would be useless, so you have to be comfortable with low 5th class rope-less climbing. We did it with no packs but a bit of food and water would have been nice.
We had no beta to go off of, and just took the route that looked best, so if our directions are unclear, take the path of least resistance, as long as it somewhat follows the ridge.
Park at, or near the Goat Creek parking lot. Hike up the Ha Ling trail to Miner's, just east/climbers right or Ha Ling. Doing Ha Ling will only add about 10 minutes, so you might as well.
From Miner's Peak, traverse on the obvious trails leading to the col at the bottom of the ridge up to Lawrence Grassi. From the col, hike down one or two hundred meters, following the still fairly obvious path that follows the bottom of the steep rock on your left. Reaching, and climbing a small 4th or 5th class climb up a face about 10 feet high. Still following the rock band trending over and down, to another small, 4th class climb up which trends left, with a cairn at the top. Follow the top of the rock band which you just climbed up, to a short, 10 foot or so 5th class climb with a boulder jammed on your left (boulder is solid, use if need be but with caution). Ascend up and right however comfortable, we chose the scree on the left side. This is about the no return point, or at least was for us, due to the unsteady scree just above a decent drop off. Head straight up toward the right of a cave you should see in the rock above you. Go right of the cave, up a scree chute and right from the top of the chute where there should be another cairn. At this point you should be able to see a dark chimney on the next large rock band, that's where you're going. Make your way toward the chimney. Start up the 20 meter, low 5th class chimney, being careful of loose holds. Keep straight up the chimney instead of taking the easier looking route that trends right about half way up. Stemming is required for the second half, so approach shoes may help (I had La Sportiva trail runners with regular running rubber, while my partner had La Sportiva approach shoes). At this point, most, if not all 5th class is behind you. Hike up to the ridge itself and climb the ridge until you can see the next band of rock. Some down climbing is necessary to get over to the band, but nothing too difficult, the down climbing can be hard to spot though so peak over the edge to find where it is, just a little down from the ridge. Traverse over, trending up, to the next, and last, rock band and make your way up one of many routes, all easy 4th class. Hike up about 20 meters to the summit of Lawrence Grassi.
Approach shoes if you aren't very comfortable on your feet on easy fifth class.
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