So, as final proof it indeed is the detune formula that makes the FM-1 sound different, I now modified the FM-1 firmware and flashed it to my FM-1.
Now my FM-1 (modded FW) and Dexed (official version, without my previous change) sound and look identical. This is again the “STR 1” patch. Top spectrogram is my FM-1 (modded FW) and bottom one is Dexed (official).
However, flashing any firmware to the FM-1 carries a risk, as M-VAVE didn’t build in a software procedure to recover from a failed FW update. Hence, I’m reluctant to share my modded FW, since I don’t want to be responsible for bricked FM-1s.