So you want a carrier that bub can lie down in?

I remember trying a padded ring sling (the Baba is pretty padded right?), and found it hard to adjust and get bub close enough to me. An unpadded ring sling might be more comfy - more adjustable, cos you can tighten it as much as you need, and as Mel said, you just spread the material across your shoulder to distribute the weight. And it won't feel as bulky either, since the padding's gone.

Another idea might be a pouch? A ring sling is more adjustable, since you'll need a pouch in your size, and you'd probably get more life out of a ring sling and it can have multiple users, but still, a pouch is a similar option with a slightly lower learning curve.
We have a pouch, that lives in the nappy bag, saves me when I suddenly realise I'm going to be stuck carrying Riv on my hip for longer than I planned! Haven't used it with the new one yet...obviously, since it's not born. If we had a ring sling, it'd have to live in the car or house.

As for trying, you never know, a Sydney babywearer might pop in, or you could check out the google group Baby Carriers Downunder - I know they have a carrier loaning program where people can try different sorts of carriers before they buy - you just need something like ebay feedback so they know you're real and legit.

Oh something else with the Baba, I know there are people who really like it, but I've also heard others who love ring slings and use them lots turn their noses up at the Baba, so I'd say that not all ring slings are like the Baba then, if that makes sense! So there's hope for finding a ring sling that works for you!