Wait....you have a place to stay...
for free...in Australia? You gotta be kiddin' me.
It would be worth running the idea up the flagpole at work to see if it flies. Offer to do some extra projects or find someone to cover for you. If you're seriously considering it, give them an incentive to say yes. You'll never know if you don't ask.
75 series trucks are cool, no doubt (I loved mine--miss it every day), but what can you do with it, really, that you can't do with any old Toyota pickup? There's no space in a ute for taxiing around tipsy college girls by the dozen. I vote against it, for that reason if no other.
On the chance that you're serious and you decide to go to Australia,
@bj70bc is right--do a lot of phone work ahead of time. Find the wreckers near where your friends are and call them. See if they have what you want, see if they'll let you cut it or at least direct their cutting while you're there. Make it clear to them that you're serious, and that you'll be there on such and such date. You'll be the crazy American. A celebrity.
Re: tools (wrenches or whatever), if you need any, you can probably just buy a cheap set at Bunnings or someplace while you're there if you don't want to haul your own. Pack them into the box when you ship it home, or donate them to a good cause before you leave Australia. Anything suitable for cutting a car body will need to be rented or borrowed while you're there.
Shipping large items from Australia can get expensive quickly. You could send it sea freight, but know that will take upwards of 8 weeks to arrive home and it won't be cheap. Another option might be to cut the sheet metal into smaller pieces (i.e. don't try to ship or carry a half-cut, instead slice it into usable sections). You could then box it and check it as "extra baggage" on your flight home. Might cost a couple hundred dollars depending on size/weight. Much cheaper than shipping and way faster. Check with the airlines for their limitations.
Finding what you need Stateside isn't impossible, but it's a much lower percentage play than Australia. Any Troopies that originated in Central or South America are likely to be as bad as what you have. Be particularly wary of any "restored" Landcruisers from south of the border. I know there's a parts-worthy red BJ75 troopy that used to live in Colorado, and was sold cheap a few years ago, but the trail has gone cold. I think I already PM'd you about it, but if not, message me and I'll tell you what I know.
And you could still pursue the new parts path, just find a better vendor and you may need to do more work finding part numbers. Just typing your VIN into Partsouq isn't going to get you there. Most parts for a car that old will show as NLA, but many parts for a newer Troopy will fit or can be adapted and are still available.