Mike
My first post so bear with me. I live in Port Augusta so know most of the areas you are talking about, although I have not done all of them (cringes with embarrassment). Not sure how you picked your peaks, but St Mary's Peak at Wilpena Pound is actually one of the best and biggest in the area. Worth the bragging rights, well around here anyway!
We have a very mediterranean climate here, so by early May the nights should cool down quite well, but the days can still reach up to around 30 degrees, particullay further north. Not sure what sort of weather you usually walk in, but walking in the heat is not very pleasant. We usually limit our walking days to those no higher than 30 degs, but that is probably more a comfort thing for us. That said, it should be fine by then. You will need to carry water on all of these walks. Water doesnt lay around for long up here! The rain tanks placed in the national parks cant be relied on either.
Looks like you will spend a fair bit of time in the National Parks, will be worth asking about the multi parks passes that are available. or try
http://www.environment.sa.gov.au for parks information.
Hope this helps
edit.....just found your intoduction and realised you will already know most of this given your an SA'er!