Thanks- so for the holes I’m using a 4mm drill for the 4mm bar, and 5mm drill for the 5mm bar- so haven’t consciously over sized the die holes. They were drilled together with the punch and die bolted tight to each other- using short presto drill bits. As the material is much less than 1mm, clearance should be tiny also- maybe 0.1mm so thought I was safe there.As @Pete. said, your punch/die clearance is too large. From your pictures it looks like the clearance is sufficient for the material to fit between the punch and die allowing it to bend down into the die hole and not be cut off. Which is also why the other holes are burred over.
Have a look at the clearance calculators on line to see what your clearance should be.
Personally I'd agree with the other suggestions to start with a single hole punch which should be easy to make to the correct tolerances, and move your material for each hole. A simple jig will allow repeatability.
Punching 12 holes in a perfect circle with 6 more in a second perfect circle isn’t easy even with a rotary table- now try to repeating that for 40 lids and you may appreciate why I’m trying to punch them using a Die