> a graduate degree may encompass both master's and doctoral degrees, which would only serve to obscure the meaning.
Nope, 99% of the time "graduate degree" == "master's degree". Usually "postgraduate degree" is used to refer to doctoral degrees. "graduate degree" is very common and generally unambiguous.
"undergraduate degree" = bachelor's degree, etc.
"graduate degree" = master's degree, etc.
"postgraduate degree" = doctorate, etc.
I've never seen people use the terms this way, and every source I find confirms what I have consistently seen in use, that “graduate degree” and “post-graduate degree” are synonyms that refer to academic (usually not professional, though that varies by context) degrees which typically require a preceding degree of bachelor’s or higher.
You should really learn about linguistic morphology.
Also, I don't think you intended it to be this way, but your inclusion of the pronunciation comes off as condescending.