Hey Marty,
Okay. I'm gonna put myself in serious danger of criticism here.
Yup, I use a large roughing gouge for.....wait for it.....wait for it.... roughing stuff round. This would include a blank as you describe. Two things. First, the post on keeping the tool rest close with minimal overhang is absolutely correct. Ya gotta keep leverage on your side and an easy mistake is to keep taking off more and more until you're hanging out there and a nasty occurs.
Second, no one every taught me how to approach the piece with the roughing gouge until well into my turning career. The trick is to drop the handle drastically until the bottom of the gouge is rubbing (or clacking loudly as the case may be) against the wood. Hint:don't do this by extending it up real high off the rest, do it by dropping the handle otherwise we're back to the overextended issue. Once you're clacking nicely, slowly raise the handle and draw the tool back until the bevel touches and then the edge. Once the edge has begun to cut wood, stop and move it side to side, changing handle angle and rotation to engage easilly in any given direction.
What you've done here is engaged the cutting edge rather than pushing it straight into the wood and using it as a glorified scraper (which is what I did all those years). This also, with a catch, will tend to push the gouge back towards you rather than lock down the edge and stall on it or break the tool. The other thing is to get some speed to the blank before you start this to prevent you from pushing the gouge into the open space as the blank turns, creating a large catch. As the piece rounds more and more, you'll find you can increase the speed and more easilly ride the bevel, making cleaner cuts. I often end up doing much of the outer shaping with the roughing gouge once it starts to cut clean.
Finally, as to the broken tang, what you do when you bend it and straighten it repeatedly is stress temper it. This makes it much more brittle and leads to an eventual break. It's the same effect as when you break a wire by repeated bending. If you have plenty of gouge left, I'd just grind the base until you have a new tang and remount it. If it's relatively new, you can spare the 1 1/2 inch of tool.
Whew, longwinded response. Hope it's helpful.
And to all the physicists and sharp spoon users out there, be gentle.
Dietrich