Excel ends up populating the plaintext as well as the HTML paste buffers. The plaintext buffer holds TSV output and the HTML buffer holds the full HTML. The HTML is the only way to distinguish between the two cells
|"foo|bar"|
|"foo\tbar"| (using some CHAR magic in excel to generate the tab character)
If you use keyboard short-cuts in your UI to copy into your app's memory but not the system clipboard then you have no way to know whether the data the user wants to paste was copied from your app or somewhere else. If you only use the system clipboard and inform the user that copy/pasting is done with right-click or key-combos and not the browser's "Edit" menu, you can handle copy-pasting predictably.
This was the most reliable method I could think of. Yes the browser's "Edit" menu is a problem and there's no way to get around that.
You probably don't have the budget to make sure this works properly as you intend it everywhere it's accessible, and by introducing it you're actively making your site, and by extension my experience, less reliable and less predictable.