Process to reset logon password for Dell SonicWall TZ600 router without erasing existing settings

As per Sonicwall's Website there is no way to do this for security reasons:

"In some instances the Administrator User Name or Password for the SonicWall Appliance may be lost or corrupted. When this occurs there is no way to reset the password or discover it as an Administrator, nor can SonicWall Technical Support provide any reset or recovery for lost Administration credentials."

Unless you have a second admin account there isn't much you can do other than reset and reconfigure.

What then is the process to reset and reconfigure the router?

There should be a reset button on the bottom of the device, use a paper clip to hold that down for ten seconds, at which point the test light should start blinking. At that point you need to go to 192.168.168.168 (you may need to set your dns statically to this subnet). You will get  a screen with several options, and you want to choose to boot the device with "Current Firmware with Factory Default Settings".

I would like to do without erasing any of the existing settings or configurations.

Not possible. Follow the video that Tyler provided, but of course you will end up back at the factory default settings.