Cleaned this up, should it be multi-trunk or other?

This does indeed look like a dwarf Alberta spruce. They are generally considered more difficult than other spruce because 1. They don't back bud as well and 2. The branches only want to grow almost straight up with little "puffs" of foliage on the tips. To get them to back bud you will have to get light into the interior without removing all the growth from any of the branches you want to keep. I don't have any of these anymore, but have lots of wild type p. Glaucoma.
 
hat said now that it is growing I understand that if I want to "try" and encourage backbudding that I need to cut back the new growth but it is unclear through my reading as to how much to let it grow before cutting back. At what point can I continue this experiment? I just cannot find a ton of material on the Dwarf Alberta Spruce.
There's a reason you don't see a lot of advice on DAS. There aren't many, mostly because they're fussy. I don't recommend them, though I admit to having 3 (2 years past rooted cutting stage, so they're not much).

You do not cutback to encourage backbudding. (On spruce at least) You allow it to grow and that growth will develop new buds. At the point where you have buds, it is then safe to cut back to them. Not before.
 
I would use guy wires to separate the trunks and help create movement. If you get some good back budding over time, you'll have something truly unique, even if other folks don't like it.
I would start feeding it like crazy next year, do not repot and hope it back buds
then suddenly one day- everything "clicks", and they begin making beautiful designs.
THIS^^^
 
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I just bought this yesterday for $10! I came across your post while researching composition ideas. The reason you don't see many of these is because they don't follow the typical rules. You have to think about growth pattern and design around it. You can't just follow the steps and expect it to do what you want it to. Bonsai Empire has a good article on spruce.

With this one, I adjusted the angle so it's not straight up. I will put a bit of an S in the left trunk and sweep the other 2 out. I recommend trunk splitters for bending the thick stuff. These guys are pretty springy too so when the split heals it holds shape better. There was a 4th trunk but it was in the wrong spot so it's gone now. Each trunk had a perfect Y that I reduced to 1. Made for good taper. You can chop these pretty hard with little consequence. Electrical tape or cut paste helps keep the sap in on the larger cuts.
 
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Here's a couple other examples of Dwarf Alberta spruce I've been working on. Top I started 2 years ago. Bottom I started 5 years ago. The tape is off now but I don't have a pic. This pic is from this spring.
 
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