Hi Andy,
Is that what you want?
Edit: Test3_Modified seems better.
I think you needed to sink your letters more inside of your cup so I made your cup slightly larger (0.1 larger in radius)
I also noticed your "i" is problematic! So I thickened your "i".
Select front & back faces of your "i" > Ctrl+C > Delete your "i" > Ctrl+V > Draw a line from center of your "i" toward center of your cup from top view > Move back faces of your "i" a little bit over previously made line toward Cup's center> Select edges of "i" faces (outer and inner) > Ctrl+C > Ctrl+V > Join them > use loft > Join all your "i" surfaces > you will have solid "i" (well there would be two solids) > Select all your solids > perform Boolean Union
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