Good day,
Two lodges that would probably give you the adventure would be Webbers on North Knife lake which is in the very high north of Manitoba. They offer Moose($14500) Caribou($10500) or a combo for ($17500). I have not personally used them but a friend several years ago went for Caribou and what he says was the trip of a lifetime. Float plane out of Thompson MB to camp.
infowebberslodges.com

One I have used for 5 consecutive yrs for fly in fishing is Jacksons Lodge which is half way up on the eastern side of Manitoba which would still offer what you seek for adventure. Their less remote prices are about half what a true north Tundra experience would be ($6800) for Moose last I saw. Bob Jackson and son Shawn run an awesome outfit with great full service camps. Float bases at Lac du Bonnet or Bisset MB about 3 hrs from ND/MB border.

jacksonslodge.com

Good Luck! Bob.