I would think you could use local bark and leaves too.
I found this list of 6 local/native? trees in the Paramatta area and if you combine it with Sally Blake’s database of eucalyptus dyes you should be able to find a colour which is agreeable to you. The colour she lists for linen is roughly what you’ll get on cotton (with a soy pre-soak).
From the list these two stand out as top candidates:
The Corymbia maculata (Spotted Gum) is a cousin of our Marri tree, which we’ve used. From what I remember from reading Dyemaking with eucalypts / [by] Jean K. Carman Corymbia bark is an excellent source of colour. Sally Blake doesn’t list swatches for the bark for the spotted gum, but if it’s similar to our Marri then the end of vassa is the time to collect the shards of sappy goodness which rub off or if you’re lucky they can be found on the ground below.
Magnolia Little Gem. This yarn, dyed with magnolia leaves (apparently they’re on Wigram st?) looks like a perfect robe colour if you could get it to stick to cotton.
Being a freelance monastic you can find a local tree which gives a good colour and make this your colour. I’m more limited as I’m trying to work backwards to get a specific colour.