Guys,
The road from Tumut to Camberra along the Snowy Mountains Highway (via Adaminably and Cooma and the Monaro Highway) is sealed all the way and and an outstanding Motorcycle ride...I ride this several time a year... I would, however be a little cautions now... 5 cm of snow fell in Thredbo (lower down the mountain) a couple of days ago... This road can get very icey or snowy very quickly... I won't be riding it gain until at least October.
The road from Tumut to Yass, via Wee Jasper (as per your route) is a great road for a 4WD or an off road Motorcycle. I drove the kids up that way a few weekends ago and it is hard work in a AWD SUV... It is in parts a steep narrow gravel track. There is no way I would take the ST on that road... Tyres would shred, every bolt would vibrate loose and the dust would clog everything!!! I believe there are plans to seal it but I cannot see that happening in the short term..
Cheers,
Doug