I heat treat 1144 ALL THE TIME. The only thing that is different is you will lose any special properties the metal had before it was heated up. And yes, I have made a punch and die from 1144. Used it on stainless too. Was not a production thing, so did not worry about its longevity. Sorry, I cannot answer your specific question on how to heat treat it. I just use a propane torch and dunk in oil. I do mostly micro machining so my parts are small, like my thumb size and smaller. A propane torch works just fine for me. And I have learned to watch for that specific color.
Edit: I do remember a loooong time ago, when I was heat treating 1144, the part would grow after HT. I switched oils and that problem went away. All is good now. Have fun…Dave