My experience with Aussie saddles is that they are "blister rigs"...for me!
The three or four I've tried just put me in a position I didn't like. Some call them the best of the English and Western saddle combinations; I find them to be the worst.
But, that's my view based upon my experience. Others have much different views and find them just fine.
If you want more "stability" but don't want the weight and bulk of a Western saddle you might look at the Plantation Saddles. Steele is, IMO, the premier maker of these. They are designed for the Walking-type horse. Steele also has a "try before you buy" program. They will send you a saddle for an extended trial (at least a week) so that you can see if it fits you and the horse and the uses you have in mind. It will be a "loaner" grade saddle (not in the prettiest of condition) but it will be fully serviceable and you won't be afraid to ride it and really use it
. My wife rode in a Steele Plantation for most of the time we had Walkers, and for some of the period we've owned Marchadors. She really liked it. It worked for both breeds.
We did the "try before you buy" thing. It really worked out well.
You might also find the Buena Vista type saddle a good option for a Walker. I see a fair number around me.
But, as for the Aussie, I'll pass.