Paper Zone is long gone. Packaging specialties was my go to for the products you are looking for. You can still travel to Redmond if you want. Impress in the University District was another idea I had but not sure if you will find all that you need. Another idea is Paper Source again in UVillage, Queen Anne and Bellevue but you may not find all you need.
I know it’s not the same as walking around the store but you can still get their stuff online. http://www.Pkgspec.com
Also, I imagine NW Art and Frame carries a lot of ribbon and cello bags. And there’s a shop on Roosevelt / 95th that sells all sorts of baking and candy making supplies It’s worth a trip even if you don’t find what you are looking for!
May not be quite the selection you’re looking for but Kelly Paper just off East Marginal Way has some of that stuff. Been a customer for small purchases for years and like the service/people there.