Replace the cat by a heli. Sounds tempting. So far I found out that the snow is rather heavy, runs are long, timberline is low and days are short.
You can do cat or sled-assisted runs here as well, to stretch your budget (or in case of weather). The further from the coast you are, and the higher your elevation, the drier the snow is. In the Chugach Range it's unlikely to be Utah-style champagne powder, that time of year especially, but our heavier snow sticks to steeper faces and is generally more stable.
Treeline around here is about 2000ft. At the Pass you'll be doing 1500-2000ft vertical runs. From town there are runs that people walk to from their houses that are 4000+ feet. By April 1st we'll have light from 6:30am to 8pm. By the end of the month it'll be 5am to 9pm. Good chance of blue skies and decent temps that time of year.
Got about 14-20days to spend. In April. Still a mid advanced rider. Still want to spend as much time as possible in the deep. Mix of sidecountry (inbound goods in resorts?), split hiking, heli.
The only large resort in the state is in Girdwood, about an hour south of Anchorage. They also have heli and cat skiing over there. Turnagain Pass, a bit south of Girdwood, is the place for splitting around there (also Hatcher's Pass, an hour and a half or so north of Anchorage). They tend to have better visibility over there in general than Thompson Pass and Valdez. There must be something good about Valdez though, or all those people from Anchorage wouldn't come over here to ride.
You could also fly into Juneau and go to Haines instead.
With that much time you could easily hit a few different spots. Maybe go down to Girdwood for a week, take the ferry to Valdez, for another week, then drive back to Hatcher's for a few days on the way back to Anchorage. It's common (for good reason) to rent an RV instead of spending money on both lodging and a rental car. The roads should be mostly okay, and I assume you're comfortable driving on snow and ice. Some of the heli packages include lodging, though. Talk to a few guide companies to get a handle on what your best option is.
As far as your skill level goes, there's all sorts of terrain accessible to heli skiers. Some of it is a little silly, as people pay for heli lifts up runs they could skin in a couple of hours from the road. Some of the front range stuff can get tracked out, but you've got lots of terrain to choose from. They'll usually take you on a mellow test run to see if you're an idiot (and make sure your gear is dialed) before taking you on more challenging runs. From what you've said in previous posts it sounds like you'll be just fine and have a lot of fun.
Look for blogs or guide websites for the areas you're looking at for pictures and videos of the various runs. The Tailgate Alaska site is another good one (they also have lots of videos on YouTube). Here's one for Thompson Pass that has good information and videos (though I don't like the guy who runs the site): www.thompsonpass.com