hello i recently found a beauty of a broad axe second hand at a barn sale for 25$ USA if you look closely at an American pattern ( pattern may be originally Swedish or Finnish i just know we made tons of them hear in the USA and you can find them all over.) broad axe you will notice not only the bent handle but unlike the Japanese pattern which has the beard but lacks a flat face this makes the Japanese axe a more Generalized tool that will carve fell and split as well as square. a traditional American pattern is dead flat on the one side to the edge and beveled on the other and sharped from only one side like a chisel. See image linked below
http://www.traditionalwoodworker.com/images/367-7505-lg.jpg
This allows you to control the cut so you can hew a beam almost dead flat as if you planed it without the axe biting into the grain as the plane of the cut can be parallel to your intended final surface and still cut the waste away this handedness of the tool of course makes it more specialized and less useful for felling or splitting but you still could in a pinch.
We also have the collector problem here in the USA people even put pretty paintings on them and hang them up on the wall a poor use for a good old tool. to avoid paying a collectors premium i kept looking at flea markets junk shops and barn/estate sales until i found one for cheap mind you it did not come with the bent stick it was axe head only and rusty and dull you can carve a handle and most farmers back in the day did if you want a really strong handle you will never find in a store look for a branch of a tree that already has the bend you want for the handle in it and carve it to final shape that way the grain will follow the bend naturally and keep it strong or you can make it straight and steam bend it when it is done.
rust can be removed, dull can be sharpened, if you have made one handle you can always make another.
also many people who hew beams also have a right and a left handed axe and learn to work ambidextrously so they can always follow the grain without splitting it out.
If i find another i can ship you one but from the frozen north of Michigan to Australia might cost as much as buying a collectors piece.
good luck and happy hunting.
Black Smith