I am looking for some further perspective regarding walking the Western Arthurs in early May (short route out via Kappa Morraine). I have been planning for an early March walk however looks like the window is closing

First things first, I have done plenty of walking in Tassie (I even lived there for three years). I know what Tassie can throw at any time of year and frankly it scares me some. Which is why I am cautious and seeking extra information.
I haven't ever done the Western Arthurs (though have done a number of other walks in the southwest including Mt Anne curcuit with it snowing all the way) and my memories of walking this time of year down there are a bit hazy

Key questions I have:
- I generally remember autumn weather as being kinder on average than most times of the year in Tassie (though s$%&t happens at any time). Our recent walks have been spring and we always end up being pinned down in tent days at some point with wind and snow. Fine - we do and will allow for some of this. What are other's experiences of May weather in the Southwest?
- Some potentially big days involved on this walk, which may be slowed down with ice/ sludge. Could be an issue with days being short. Times reported seem to be very variable. Any further opinions on realistic times and under what conditions?
- I have found notes of a number of so-so camps if necessary along the way, but there also seem to be at least two committed days (between Lake Oberon and Haven Lake) with little options to hunker down before the final destination. Anyone have differing advice?
- What is the scrambling like with a bit of snow and ice? We'll take crampons and maybe ice axes (not sure if much use given it will be mixed stuff and likely just sludgy). But given the short days we'll have to be moving - if there is likely to be anything more than basic occasional ropework for haulage etc, then I can't see the route being a great idea that time of year.
Also, we are both fit and strong walkers, with ropework, climbing and snow experience. We have top-notch gear all round. But I am not taking on this walk that time of year without a good plan and good get-out options. And even with this, if the forecast is not good on arrival (if we do go) we'll have to divert to something else instead.
Thanks in advance.