I'm not entirely sure if you are using a Weldment Cut List or a Bill of Materials. It is possible using a BoM table type as you can add equations to control the column:
In this case the Process 1 and Process 2 columns are driven by custom properties, while the "Final Process" column is controlled by an equation:
IF('Process 2' = ""; 'Process 1'; `Process 2`)
You can then hide the other Process columns if needed.
If you need to created nested if statements for more than 2 properties, see this forum post: https://forum.solidworks.com/message/190994#comment-190994
Hopefully that gets you what you are after.
Yeah that works! I just had issues with the syntax, but once I sorted that out it seems to work. You mentioned this in your post but I'll just reiterate it: you must have all the individual process columns in the table (hidden is fine). You cannot just link to a property it seems.
For reference this is the equation I used:
IF('Process 2'="";`Process 1`;IF(`Process 3`="";`Process 2`;IF('Process 4'="";'Process 3';IF('Process 5'="";'Process 4';IF('Process 6'="";'Process 5';'Process 6')))))