You're optimistic about the snow coverage this year
I believe technically the ACT side requires a permit as it's in the Cotter catchment. No such restriction in NSW.
Off-hand, if you wanted to get further than Pryors -- the footpad up Gingera initially follows a small creek up to a small clearing on a shoulder. Water, below treeline, fairly flat. If you were to carry water or melt snow, you could probably find a spot up on the summit ridge back towards Pryors. A lot of scrub & rocks there to hide behind.