Not sure I have one of those readily available, i do have it under some heavy stuff currently. But yea i cut the bottom of the barrel off and split it in half so trying to make the halves flatter and less curved.
Perhaps try boiling water, applying some weights, then pouring the water over the plastic?
Or soaking some towels in the boiling water and draping them on, then applying weight? You can then pour more boiling water on the towels as needed.
So, yeah, then go with the hot water method. You can always fill a bathtub too. That one might fly more if you get her a spa day for the same day you're going to work, and clean it real good when you're done though.
Googling suggests heat gun, hair dryer, boiling water, or an oven. But it warns that its really easy to over do it in the oven and burn it. Another suggestion was once you get it hot enough to shape, shape it and then dunk it in a barrel of water to cool it quickly. One comment suggested cutting it out of the barrel, and then doing the shaping only on the piece that needs shaped. But I could see how for a breastplate that's a big area to heat at once. Another said to try to use the natural shape of the barrel as much as possible.
The key is to get the pieces close to the size you need and weights. Less surface area mean less conduction. Cutting the barrel in half at least would make your job much easier. Make sure to remove the capture ring at the top and the full curve of the bottom. Place a half down with blocks (or some other weight) on one of the cut sides and slowly heat toward the other end in a top to bottom motion. It will take a long time. Take this with a grain of salt as I have never worked with a barrel but I have worked with a bit of schedule 40 PVC pipe for armor.