Can't upload new sketch due to the existing sketch

Your sketch stops at the moment that avrdude opens the serial port and asserts DTR to start the upload. That will reset your board and the bootloader is activated and your sketch is not running at that moment. So your scenario is highly unusual.

The bootloader will be active for a few seconds if no data is transferred or will stay active during the upload.

Burn the bootloader. You will need a programmer or an other Arduino that is programmed with a programmer sketch.