Doug -
For what it's worth, I have the System 3 version of this set, built in either November 1980 or 81 (the tag has fallen off the back of the set and I am reading the imprint left in the glue). It looks nearly identical to your set, and has a 6-button remote - power, channel up/down, volume up/down, and mute. The only identifying marks on it are a tag in the battery compartment that reads:
0446QR
EIA 343 Mexico
124-16
and on the battery door:
24-2685
1
"Replace with Zenith battery 5-115 for best operation"
The remote is in the first picture in the following thread, top row, second from right.
http://www.videokarma.org/showthread.php?t=246014
-Jim