Donnachaidh,
I am not sure where you are located, and if you are looking for a European moose hunt, or looking to travel elesewhere. If you want to hunt the biggest moose (Alaska-Yukon subspecies), you'll have to travel to Alaska, or to Canada (specifically the Yukon or the Northwest Territories).
I hunted with Stan Stevens/Mackenize Mountain Outfitters in the Mackenzie Mountains of the Northwest Territories back in September. The have some monsters there, and it is essentially un-hunted every year as Stan has a 9,000 square mile (23,300 sq. km) concession and only takes about 14 hunters per year to hunt moose specifically. We had 7 hunters in camp, and all took excellent bull moose with 3 approaching the 70 inch mark. There were a couple of moose seen from the air that would have gone well over the 70 inch mark. You can also add Mountain Caribou as well, and they have some of the biggest mountain caribou in the world in the NWT. Their were some very nice bulls taken. I struck out on the caribou however, because it took me a while to get my moose, and the migration was occurring in earnest a little farther south from our remote outpost. I can recommend his outfit without a doubt, and he has a very solid reputation (40 years outfitting). However, a disclaimer.......
It is very remote, cold and wet. The terrain is that God-forsaken tundra/hummocks that make it miserable to walk on. Couple that with the fact that these 1500+ lb moose think they are sheep, and you have to climb to get them, and you've got yourself the making of a superb adventure. It's a back-pack style hunt, and you stay in back-pack type tents in sleeping bags, but Stan also has a nice base camp for when you return. Stan is old school for sure, and as tough as they come. Like 375 Ruger Fan said, the fun is over when you realize the magnitude of the animal you have put down, and that you have to get him squared away in the cold and wet. The nice thing about Stan's outfit is that he has a helicopter, so once you get the moose skinned, quartered, deboned, and packed out to a suitable landing site, he comes and gets the cape/antlers/meat with his Robinson R44 helicopter which makes it much easier than having to pack huge hunks of meat long distances.
Eventually, if I can motivate myself to finish writing up my report, I'll post the hunt report on here.
This video is from a German hunter, Henrik Lott, I like to watch on YouTube. I really like his videos. Anyway, he hunts all of his animals with a Kreighoff Double Rifle add open sights. He hunted in the NWT for moose with a double. He hunted with South Nahanni Outfitters. The scenery is really cool, and it gives you an idea of the terrain.
Anyway, let me know if you have any other questions and good luck on finding your moose hunt.