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A 15 Amp power supply would appear to rule out any problems with power.
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I'm not sure about your description of the connection between Nano pin A2 and your module. I'm guessing that this is (somewhow) connected to POWERKEY/PWRKEY on the SIM7600 module.
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I don't understand the problem with the enhanced debugging since that writes to Serial just like the other commands which have written to the serial console. The first thing to suspect is that the file you have modified is not being used by this sketch and maybe there are multiple versions. Rename it and see if there is a complaint at compilation time about it being missing.
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I've found this documentation for a DFROBOT SIM7600 module which includes as schematic, instructions and some simple tests. SIM7600CE-T_4G(LTE)_Shield_V1.0_SKU_TEL0124-DFRobot . Is there anything similar for your module ? Some of the tests could be useful. The only thing I noticed is that Software Serial is run at 115200 baud, which is really too high, and the SMS test requires a termination character of 0x1A. Their [DFROBOT's] serial console supports this so maybe try that.