Woodworking somewhat translates. Acrylic when bonded is actually welded together with a solvent so the pieces become one. In most cases, the joint is actually stronger than the material, if you take 2 pieces and bond them, let them cure, and then try to break them you'll break the sheet not the joint. So a crack that has formed in the top sheet that reaches the joint can translate down into the back panel easily.
You can laminate a sheet right over the top of the existing top, and that might work OK but who knows for how long. You can brace on the inside across the crack also but if you don't stop the crack, it will eventually spread. If James was feeling up to it he might be able to respond better but he's staying off the forums for a while.
As far as taking it to a plastics shop, unless they work on aquariums I wouldn't trust them any more than a DIYer. Aquarium work is a specialized subset IMO and most acrylic shops don't know it well enough. It's not that easy to take the top off an existing tank and put a new one on correctly esp if you've never done it before, x2 with a tank this big.