Here's a thought. How about a Winchester 1895--a classic lever gun favored by none other than Theodore Roosevelt and the Texas Rangers at the start of the 20th century.
Miroku has been producing them off and on under both the Browning and Winchester name. I think they started producing under the Browning logo back in the late 90's, and under the Winchester logo once Browning/FN Herstal acquired the license.
You've got choices of .270 Win, 30-40 Krag, 30-06, and the beefy .405 Winchester. Miroku is not currently producing, but there are quite a few still on the auctions sites--many still new in box. I'm assuming you might find them down under too. The .270 Win is hard to find since they were only produced for short time.
The 1895 was the last rifle lever action that John M. Browning designed for Winchester and it is unique in that it eliminated the tubular magazine in favor of an internal box magazine enabling it to handle military Spitzer styled bullets like the Browning BLR does.
You do not have a removable magazine, but have to load the rounds one at a time through the top of the open receiver. It is also top eject only, so sight improvement is limited to receiver or tang sights such as the Lyman or Williams.
You are looking at $1,000 to $1,300 USD in most cases, but that's less than a Uberti 76, which you were first considering. The prices might even be better in Oz since you are a bit closer to the source.
Bottom line is if you can find one in 30-06 cal or a buffalo stopping .408 Win, you will have your classic lever gun that is less rare than an 1876 and maybe just fill in that spot between the 30-30 and 45-70.
Cheers