The thing with Alaska hunting is logistics. There are many things that most people don't think about, either the time it takes, or the cost associated with it.
You could "hunt" moose for $2000, but you probably won't kill one... and will likely see a number of people since you don't have the luxury of knowing where the pressure will be, probably won't find/see a legal moose due to timing, rutting area locations, what habitat they prefer, access, etc. It would take you a few years to sort it out, IMO. You can't just shoot any bull you see, it must have 4 brow tines, or be 50" wide. This maybe 1 in 10 bulls you see, or less.
Assuming your budget is from the time you step off the plane in AK, and buy a tag/license, you're left with about $1000.
Vehicle rental will run you about $6-700+ a week. Not sure on supplies/gear you'd want to get or rent, and shipping meat/antlers home will cost you hundreds of dollars.
You might be able to find a taxi to fly you in for $1000, but it will probably cost you another $1000-1500 to fly out your meat and you won't get far form town. Taxi's start at $400/hr and go up from there. You pay for all the airtime to and from your destination. So if you were 30 min out by air, you'd pay 2 hours flight time for a drop off and pickup. You will be lucky to make it 10-15 miles off the road system in 30 minutes of flight time, depending on where you start from... And highly unlikely you'll have it to yourself.
There are places you can hunt off the road/highway for moose, but expect to pack one 3-5 miles through some squishy, wet, river crossings, muskeg, thick alders AND in areas where you can get away from the ATVs...thats if you even found one. I see 2-4 legal bulls every year "near" the road, but so far I haven't wanted one bad enough to pack it out from the spots I find them. I've seen some giants too, but just couldn't convince myself to do it, and I'm pretty stupid when it comes to packing stuff a long ways... Many people think they have what it takes, until you really need to do it. Its easily the hardest thing I've ever done. I've packed about half a dozen moose out, the farthest was almost 3 miles, but it was all down hill, on solid ground. I've packed a few in the 2 mile range through absolute chit, and it sucked. If I was a NR I may consider packing a moose 3-4 miles, if it was my only moose hunt and I was in shape enough and mentally prepared to pack 3-4x 80-90lbs, with no trail, for multiple days.
Also you need be realistic about it... it will take you 3 days to get it out assuming 2 guys that are fit. Some areas require you leave the meat on the bone, which will add 2 more pack loads... and you will need to deal with meat prior to leaving AK, and also spend the time to hunt. A week would give you about 3 days of actual hunting including travel time...
Could you do it for $2000, sure. Will you kill one? Doubtful. Will it be fun? That depends on what you want to get out of it. It certainly won't be the experience you hoped for on a once in a lifetime hunt, and there will likely be a lot of additional costs you didn't think about. Will you see some amazing country, you bet.
I have a moose hunt planned this year that will cost me a couple tanks of gas... and about $5000 in packraft and ATV... haha. Also have another couple spots that will cost me half a tank of gas, but I don't expect to kill one, much less see a legal bull, but thats ok with me.
