Thanks for pointing this thread out to me Magnus. I'm rather shocked by the range of advice you've gotten in it both good and bad thus far, particularly from arborists completely unfamiliar with the treacherous hinging characteristics of eucs in general.
Unless a euc is pulled over exactly 180 degrees opposite it's lean, it's not going to hold it's hinge long enough for it to get past it's vertical balance point and fall anywhere near where you want it to at all.
They are one of the most treacherously weak hinge holding species of trees around, their wood grain is so convuluted that the only wood splitters capable of splitting it are the larger models due to their raw HP and shearing ability.
Another important factor in pulling over eucs is finding a bull line tie point in the tree that's centered over your face cut below it, and of sufficient size and strength to withstand the tremendous amount of pulling force exerted on it to pull it up and over center. If for any reason that pulling point fails, you and your house's well being are in serious trouble. If the tree is 30 inches DBH then any tie in wood under 12 inches is getting a bit iffy in a euc.
To gain enough pulling power with your winch to get the tree safely over center will probably require placing a heavy duty steel pulley in the tree at the pull point so you can double the pulling power on your winch.
And for heavens sakes don't do any kind of cutting at all on the tree until after your rigging is set up and you're exerting 2-3K lbs of pulling force on the tree with your winch!
A typical western face cut with about a 60 degree range comprising 1/3rd of the tree's dia is fine, gunned straight at your winch. Your finish cut needs to be at the same heigth as your face cut's apex, and be perfectly parallel to the apex's axis. Leave at least 3-4 inches of hinge on a euc of that size, back your finish cut with wedges. Work in conjunction with your winch operator by either radio or cell phone. At 4 inches of hinge have him pulling for all he's worth, if you see a little movement at the pulling point in the tree in the direction you want, cut a little more in the finish cut to a 3 inch hinge, but no more. Once it's over center and falling, that 3 inch hinge won't hold for long at all, maybe 20-30 degrees past vertical if you're lucky.
So unless you can set up wour winching point exactly 180 degrees off your tree's lean, with enough winch line to pull your compound bull line twice the distance needed to get the tree over center and falling in the right direction?
Don't do it, not with a treacherous euc!
The trees in your pics don't look to me like they're any kind of imminent hazard at all Magnus, so take your sweet time and try to fly in an expert to do the work as barter for free lodging at an exotic island vacation point!
Whatever you do, be careful and have a clear escape route from the base cut in case a rope snaps or any other failure occurs.
Getting a pro in there to do it for you is your very best choice, particularly when your working those treacherous Australian weeds down.
Good luck Magnus!
jomoco