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Check out this Tableau knowledge base post on Top 15 LOD Expressions Top 15 LOD Expressions | Tableau Software
Section 4. is called "Percent of Total" and it describes a way to do % of Total calculations using LOD calculations that are not affected by filtering. It has a step-by-step example that should help you with your current workbook.
If you took your current filtered version & added an LOD calculation to the same worksheet, you would be able to see side-by-side percentages (filtered & global).
Thanks for the quick response!
I briefly looked at LOD expressions but was not using the exact syntax required for my specific issue, so I had moved on from it too quickly. Your link containing the forwarding link to the syntax options helped completely. I needed to use the FIXED option. Perfect!