I then, say to myself, "Okay, I'll just turn it into an MP3 with my "dbpowerAMP Music Converter"." Turns out the version I had didn't support the format either. So, I go to the "dbpowerAMP Music Converter" website, and lo and behold, they had a newer version which supported that format, so I updated my older version. According to the converter's website, .mpga is a new compression technique called MP3Pro. Instead of MPEG 1-3, it encodes a MPEG 2-3!
Anyway, to make a long boring story short, I can now convert those .mpga files to regular MP3's and drag them into Easy CD Creator to make audio CD's out of them, so I am content again! :-)