I have sent several different furbearer hides to Moyles and they have all turned out great with a quick turnaround. I know of a person who sent a cow moose to them last year and they said it turned out great. I don't think Moyles takes raw fur so you will need to flesh, stretch, and dry it. My friend said her biggest problem in sending them a moose hide was that you had to re-hydrate the back of the hide after the drying. The hide on the back is very thick and would not fold without re-hydrating it.
I have used Montana Rug and Tanning for my most recent larger hides. They have done a caribou as just a tan, a full grizzly rug, and are just finishing up my mountain goat throw/blanket. Everything has turned out great so far. Montana rug and tanning will also take your fur raw and deal with the fleshing and stretching.
I would recommend doing the throw/blanket with a moose hide if yo're not planning on making clothing out of it. Tanned hides from anything larger than a wolf or lion are just awkward and kind of an eye sore IMO. They don't lay flat so the only option is to hang them over furniture. I'd recommend having the taxidermist square/round off the hide so it lays flat and looks good, add a matching backing, and trim the backing flush with the hide. Then you can lay it out on the ground, on a bed, use it as a blanket, etc.
If you ship it raw, throw it in a couple contractor bags and then wrap it in visqueen. Then just place the wrapped hide into a large tote and throw the whole works into a huge freezer for a few days. It should stay frozen during shipping. Ship it on a Monday and do guaranteed one or two day. Let the receiving end know its coming so it doesn't sit on their dock. The shipping on a heavy tote with a raw fur might be cheaper than a rectangle box than stands 6 feet tall and a foot wide with a stretched hide. I shipped a grizzly hide from AK to MT next day at UPS and it was only about $100. I think it weighed 80 lbs.
I know you asked about prices, sorry i can't help there since I haven't done a moose (yet). Just figured I would throw in a couple points to ponder; don't want you to spend the money and not get what you were expecting in the end. I would expect to spend around $600 after shipping. Hopefully you share with us whatever the finished product is for future reference and I hope you enjoy whatever the finished product is that you decide! Congrats on the full freezer!