Ski Utah Interconnect Adventure.
Little Cottonwood Canyon (Alta, Snowbird), Big Cottonwood Canyon (Brighton, Solitude) and the back side (Park City and others) has 5 world class resorts that as the crow flies are very close to each other. There is a program where you can go with a guide and tour with them.
I have not done this but have friends who have. Its a lot of work since your going to be skiining and hiking a lot. But your at the famous Wasatch backcountry.
Alta has a seperate area next to the resort in Grizzly Gulch Bowl reserved for cat skiing.
You need to reserve for it and will cost considerably more than a lift ticket but less than a day of heliskiing.
It has over 300 acres, guides, heated seats in the catmobile. All day catskiing not jut one run.
This is an option if you really want your own space for virgin powder.
Wasatch Powderbird Guides has an operation in the surrounding mountains. You actually pass them on the way up to Alta and if you stay at the Cliff lodge or rental homes, you can see them land and take off at their property. You are paired into a small group with a guide by ability.
You want to experience heliskiing but cant afford a whole week in Alaska or are afraid of the experts steeps and snow? This might be a perfect solution for you. Check them out and call to talk to them. They are very helpful and can assist advanced intermediates and up to have a wonderful time.
Heli Skiing is a thrill but very expensive. You have 4 to 5 runs in a day and have powder turns and no crowds.