I doubt many nurseries are able to issue phyto certs in Sydney, and I think finding one with finger limes would be extra tough, as most grafted varieties stock comes from only a couple of nurseries between the northern rivers and sunshine coast, and non-grafted finger limes are mostly found in smaller nurseries. (And why would you go to the trouble of exporting a non-grafted anyway?)
Unfortunately the Aus Citrus Propagation Program doesn't have finger limes, so there aren't any official channels to go through either.
I'd try contacting AQIS (or whatever it's now called) directly to see what the options are for getting one and putting it through the process by a third party. I can't imagine it would be cheap though. It may be worth contacting some of the wholesale finger lime nurseries (up north) for their take as well, but I wouldn't hold your breath on them.