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Now I've tried it out and it worked for the edges I've talked about. But your method caused another problem: I can't adjust the bevel width for the other edges anymore when the width reaches a small number like 0.05. So the rounding is very small.
Sorry, but for me this doesn't work. Maybe it has to do with your geometry: in the corner you have a square but I only have this one diagonal (see the first picture) How did you get this square?
I applied the bevel modifier and set the crease for the three edges to -1 but it didn't work. In this state, I tried again using EdgeSplit and marked the edges sharp but no changes.