Can you post a close-up photo of the crack? I also have a cracked BW tank. Mine is around the flange fitting. Apparently this is a not to uncommon failure with these above floor tanks due to having the weight of the toilet directly above and not enough additional surrounding relief for the flange fitting. Unfortunately, a PO attempted to patch with silicone-- woefully inadequate.
I will be trying to plastic weld mine. Seems your tank is polyethylene, as is mine. I have researched the topic and methods and know just enough to be dangerous. But I figure it's worth a try before I scrap it. If interested, here is some pertinent info: 1. Epoxy & Fiberglass patches won't work (according to experts) 2. Like sticks to like: must be exact type of plastic (eg. low density polypropelene to low density polypropelene 3. Different materials have different optimum working temps. 4. Drill small holes at either end of crack to prevent migration & weld. There are a few seemingly good U-tube vids using plastic welders to soldering irons to torches. With a clean crack it may be possible to clamp it together and weld the seam together without additional material, although that would probably require a big leap of faith.
One potential drawback for you is that the crack is on the bottom and will be subjected to stress at all times tank is used. Mine is at the top, so if properly supported (which I plan on), needs mostly just a good watertight seal- but extra reinforcement will still be given, of course.
I bought some polyetyhlene cutting boards to practice on and, depending on how that goes will start working on the tank. I'll post about it as I go.