I like your approach and lapping film is waiting in my desk to give it a try.
For the sake of having correct figures for prosperity...
hardened steel is not 7.5 Mohs, according to my sources:
eFunda: Convert Hardness: Rockwell C-Scale
On the Rockwell C scale, which is what's generally used for cutlery, HRC 64 = 6 mohs. HRC 58 = 5 mohs. Both are exponential scales, so the differences between one point and the next are rather huge.
One thing that's not clear to me: how do I keep the film from not moving around when the sheet of paper sits between the tile and the film. I understand that the film sticks to the tile with a bit of water (air bubbles to be avoided). But how do I keep it stuck with the paper sheet in between?
Thanks,
Bart.