No - it is not a plot-hole.
Joe is not perceiving time as 1000 years a day. He is perceiving time as normal, within the confines of the cookie. The cookie includes the cabin, the radio, and the environs.
The song is not playing in real time. It, like everything else in the cookie, is perceived by Joe to be normal.
If you were to listen to the song in the real world, you'd hear it as a blip.
Remember, everything in the cookie is experiencing time at the same rate.
Basically Joe's consciousness is trapped in an eternal virtual world. From his perspective, the day repeats itself over and over, forever. The song repeats itself on the radio. Joe never ages, never dies, cannot escape.
The 1000 year thing comes from outside the cookie. For each day that occurs in real life, the cookie (which contains Joe, the cabin, the radio, the song, etc.) runs a 1000 year cycle. That is, a "day" for the cookie is 0.004 seconds in the real world.
The entirety of the cookie experiences this, not just Joe. For Joe, everything is happening at a normal pace. He experiences 24 hours a day, seven days a week. It's just that the same day is repeated ad-nauseam. He has no idea that each day he experiences is only 0.004 in the real world. He has no idea that he will be trapped there for thousands of years.