The 2 larger radii need to connect with a smaller radius, not a sharp corner. You also need a radius all along the top edge. Everywhere there is a sharp corner needs to be replaced with a radius. I have an idea how to form these without a press, but will require manual trimming and hole drilling, and this could be done on a mill with a hold down fixture.
I pondered this for the last few hours and remembered a project I done over 40 yrs ago.
This is definitely out of the box thinking, but it works because I have done it. I'll probably take some crap about it, but it works.
It's called "fire forming". Back when I was in jr. high school shop class, our instructor was into flintlock rifles and such, and built many by hand "old school". He had a lot of unique methods that he taught us. One of them was fire forming, a process he used to make powder flasks.
One of the projects we done was a copper ash tray that was formed in a die with black powder.
The die simply used a cavity formed like an ash tray, about 1" thick steel block. The copper sheet was placed on top of the cavity, and a 1" cover plate was bolted down to the bottom die. The top had a threaded hole in which a steel nipple was threaded into. We used 15 grains of FFF black powder, and set it off with a percussion cap, using a ball peen hammer. Once you unbolted the 2 halves, you had a perfectly formed ash tray. You then trimmed the outside with shears and finished up with a file.