If you are a competent/confident driver you can go via Tom Groggin and Thredbo.  No doubt there will be nervous nellies come on and tell you not to go that way. The road is not particularly steep. The stretch from Tom Groggin to Dead Horse ap is fairly long an has many curves, some of them tight, the shoulders are narrow. Three of us came down there some years ago, the largest van was 24' and none of us had any problem keeping to our side of the road. The steepest part of that route is actually just after the Murray power stations and not the "dreaded hill." The narrowest part of the road is also along that stretch.

Your rig will have no problem negotiating that road. After you have passed through the national park there is a long downhill stretch or three. Slow down and select as low a gear as you can to preserve your brakes. If you don't then you will be at mor risk there than the uphill sections.