Hi JIC - In regard to holding the piece for machining. If you can put some holes in the part that are either needed later or are just holes , then use standoffs to bolt the part to the machine bed this is a better less stress hold then in a vice. This part is assymetric and all the weld are on one side. Its unlikely it will settle out flat by machining it. Creeping up on "flat" from both sides you may never get to flat You could try cold setting it if you have a press that can bend it? Thermal SR is the go. Are there potters or kilns around your way? Its a small part and they will get to 650C easy....Peter

if you do oxy or torch it use a soft flame and keep it moving and try to bring the whole thing up to temp. Last resort thinking about it. You may warp it worse need an oven or a kiln that can bring it up slow and down slow...

Did a bit of reading and mild steel will relieve as low as 200C so you run your kitchen oven flat chat and cook it for a few hours and see how it goes!! Even grit blasting can relieve it a bit if there's a sand blaster around your way?