I had the same issue with my hull of the Pittsburgh, but heating in hot water did not solve the problem, even when using clamps to "force" the keel to be flat. Since the rest of the kit seemed decent enough, I solved most of the hull warpage by doing what you were reluctant to attempt -- used a hacksaw to cut into the keel (hull inverted) down nearly to the main deck, then bent the two halves together and glued them at the keel and filled in the gap with putty. If you are concerned about resin dust, just wear a dust mask (you must have saved some of them from the Covid-19 pandemic). The stern was still slightly warped upward but I did not consider it a major problem. You can see the result of my work at this URL:
http://www.modelshipgallery.com/gallery/ca/ca-72/Pittsburgh-350-ra/index.htm 
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I used a massive pot, really huge, and I got some of the bend out. I recall that at the time, the supposition was that ISW had used the plans from the Floating Drydock which printed with that upturned stern, although it wasn't correct that way; it was a printing error. I don't know if that's true, but that's what modelers said at the time.
If you get a hull like that, another option would be to use a cutter and make little slices in the hull, port to starboard, and then use those as almost like an accordion to heat and bend the hull back flat. Then, fill in the slices with your putty or filler of choice. I considered doing that, but was afraid of the resin dust.