S7 or H13 for 304 forming die

Speccing a small two‑station forming die for 0.090" 304 on a 30‑ton OBI, I’m torn between S7 and H13; I plan to harden to 58–60 HRC, leave 0.002" for grind after heat treat, and I’m chasing edge life without chipping — what’s your real‑world pick and why? For the punch tips (R0.015), would you tweak temper or surface finish (stone to 8–12 µin Ra) differently between the two?

‌⁠‍⁠​‍​‍‌⁠‌​​‍​‍​⁠‍‍​‍​‍‌‍‌⁠‌‍⁠‌‌‍‍‍​⁠​⁠​‍​‍​‍⁠​​‍​‍‌‍‍⁠​‍​‍​⁠‍‍​‍​‍‌‍⁠‍‌‍‌‌‌⁠‌⁠‌‌⁠⁠‌⁠‌​‌‍⁠⁠‌⁠​​‌‍‍‌‌‍​⁠​‍​‍​‍⁠​​‍​‍‌‍‍‌‌‍‌​​‍​‍​⁠‍‍​‍​‍‌‍⁠‍‌‍‌‌‌⁠‌⁠​‍​‍​‍⁠​​‍​‍‌‍‌​​‍​‍​⁠‍‍​‍​‍​⁠​‍​⁠​​​⁠​‍​⁠‌‌​⁠​‌​⁠​‍​⁠​‌​⁠‍​​‍​‍​‍⁠​​‍​‍‌‍‍​​‍​‍​⁠‍‍​‍​‍‌​‌‍‌‍‌⁠‌‍‍​‌⁠‍‌‌‌​⁠‌​⁠​‌‍‍‍​‍⁠‌‌⁠‌‌‌​‍⁠​⁠‍‌‌​‌‌‌‌​‍‌‍‍‌‌⁠​‌‌‍‍​​‍​‍‌⁠⁠‌​