Snow overnighters in Alpine NP

I’ve about maxed out my Baw Baw NP enthusiasm for this year, and it has just occurred to me that many of the choice hiking areas in the Alpine NP are now off limits due to seasonal road closures. I was really keen to get the snow-shoes on at Mt Howitt but don’t see how I can get there. From my reading of the maps, access to the Lake Tali Karng trail should still be achievable, Mt Stirling is a goer but at $120 to park overnight it is a bit of a costly sleep outside..
Any other suggestions for 1-2night hikes with snow camping within a couple of hours of Melbourne without a) paying entry fees and b) other people
I have a 4WD and chains. Back of Cathedral/Lake Mountain/Mt Margaret area is a day trip option but maybe not reliably quiet overnight, as I believe there is year round 4WD access to Keppel Hut and the surrounding tracks?
Any other suggestions for 1-2night hikes with snow camping within a couple of hours of Melbourne without a) paying entry fees and b) other people

I have a 4WD and chains. Back of Cathedral/Lake Mountain/Mt Margaret area is a day trip option but maybe not reliably quiet overnight, as I believe there is year round 4WD access to Keppel Hut and the surrounding tracks?