Like I said, you can put in small lateral correction with heat as long as you clamp on some side pieces of hardboard etc to contain the heat on the belly. Clamp it up with 1" of sideways bend apply heat over about a foot in that centre section, just a minute at a time over a 3" section at a time, so it doesn't take too long.... let it cool for an hour, job done.
I apply a couple of layers of masking tape along each edge before clamping the hardboard strip to really make sure there is no hot air blow by.
If the hardboard, hangs down beyond the belly by about an inch it channels the hot air along the belly giving good even warmth.
I'd make sure the bow isn't thicker than it's wide at any point too, that really makes it try to go sideways.
Del