Two of your choices are UPS http://www.ups.com/content/au/en/contact/index.html
and DHL (look them up for comparison).
You may also be able to use the United States Postal Service.

I would say that the cheapest option will be to simply pay the excess baggage fees. Short of that - for example, you don't want to schlep your items to multiple destinations - then the US Post Office will be at least as cheap as FedEx or UPS and would be my first stop.

If you are talking about a semi-reasonable amount of 'stuff'- I agree w/ travel gourmet. Buy a large/cheap suitcase (Walmart/K-Mart or even Goodwill) and pay the excess baggage fees would be the cheapest for shipping.

Otherwise - the US Post Office will be cheaper than UPS/FedX. All 3 will cost more than baggage fees if you are talking about substantial weight.

I'm laughing because I was just reading your trip report and I already had guessed you were going to run into this problem!

We used to come home from Switzerland and try to take half of America back with us in our luggage. We learned to pack very light on the way over and bring an extra suitcase for the way back.

LOL. You could always "layer up" with clothes when boarding the plane, eh?

This somehow reminds me of the Aussies we traveled with in Europe (Morocco, Spain and later met up at Octoberfest after we three went to Greece) - and back then anyway - many Aussies (and Kiwis) traveled all over - for a year at a time - and bought a Van, ski equipment, etc, so they had to figure out ways to send stuff home.

One ld from Melbourne had even gone to India on "shopping trips" - and found some great deals on gold and jewelry - so when returning to Australia - at your "customs", he dressed up in the wildest outfit he could find, with all the attendant jewelry - and acted very "swishy" - and waltzed right through without having to pay any duty.

USPS may not be cheaper than FedEx. I'd pay the excess baggage charge as has been suggested.

The large USPS flat rate box sent to Australia (group 6) has a weight limit of 20 lb. and costs $60.95.
You decide if you want to carry 20 extra pounds with you all the way through several airports or have it waiting for you when you get home.
If your airline does not charge more than $3/lb. total to get your overweight bags back to Australia, you can carry them.
Have you priced the other options ? (UPS, FedEx and DHL)

We price checked all the options when traveling to Chile for a wedding from the US, shipping dressy clothes ahead, and USPS large flat rate box as mentioned above was by far the cheapest.Ironically, it was delivered by FedEx and arrived there in three days.
I have also bought many cheap bags to carry things home on the flights when traveling internationally. The I donate the bags to Goodwill if they are still in one piece.

If you need to get another suitcase, look at places like Target, Ross, Marshalls or TJ Maxx.

Go to an Army Navy store--OR WalMart and buy a canvas duffel bag in the camping department. No weight to it and can pack a lot. Personally, I'd prefer a new one to Goodwill or such with the bedbug problem--and other things! LOL

"You decide if you want to carry 20 extra pounds with you all the way through several airports or have it waiting for you when you get home."

You must not fly 'legacy' airlines much (you really have to try something other than Allegiant ). One can check their bags all the way through.

"The large USPS flat rate box sent to Australia (group 6) has a weight limit of 20 lb. and costs $60.95."

A large suitcase weighing 50 lbs or more would only cost around $50 (depending on the airline). MUCH less than $60 for 20lbs.

Not sure what you have purchased, but if it is valuable or you would hate to have it stolen, then carry it on if allowed or ship it home. If you put it in a suitcase, it cannot be locked and any valuables could disappear.