So, to explain why I failed to find a minimal working problem - apparently it's not the Texture, or the original images - Sprites made from both are running. There's no discernible cause for this, no condition that I could isolate through prints, etc. Frankly, at the level of information open to me, I can't discern any difference between the Sprites that crash (and they're very few) and those that don't.
The only thing I know is that sometimes, when calling line 165 in Sprite.Draw, states.Transform *= Transform, the "right" variable will be null. Since this.Transform isn't null, but is Matrix(System.Single)[], I don't really understand what is happening.