The Most Economical Method to Ship a Heavy Box to USA

Hi guys & girls,

I have sold quite a bit on eBay over the years to both local and international buyers. Recently I sold an item which is somewhat odd shaped and also on the heavy side to a buyer in the USA and I'm having trouble finding a shipping service that won't charge me an arm and a leg due to it's size and weight.

After the packaging is done I have a box that weighs 22Kg and has the dimensions 60x60x15cm

I have explored the usual options;

Auspost - Can't use as the max weight is 20Kg and should have a girth of 140cm (width+length)x2
PacknSend - Online quote $199
Sendle - Don't think they do over 20Kg

I would believe DHL and Fedex would end up being too expensive.

Therefore I'm fast running out of options and to make things worse I only charged $110 for postage (Still I would not mind paying up to $200).
So I was wondering whether there is someone here who has had any experience in the past making once off shipments internationally, or specifically to the USA.

I'm looking for the cheapest(as I'm posting a $800 item) shipping method with tracking and speed is not a major deciding factor.

Any helpful advice would be appreciated.