Just downloaded the episode with William Shatner and Grace Jones from Usenet. There are a few different episodes, not the complete series.
The Original Max Talking Headroom Show - EP1 - Jerry Hall
The Original Max Talking Headroom Show - EP3 - Ron Reagan Jr
The Original Max Talking Headroom Show - EP4 - Dr Ruth
The Original Max Talking Headroom Show - EP6 - William Shater
Have you got the two series from 1987? They are on Usenet, but my file retention is only 1000 days. Those episodes were posted 2010.
Edit: There are various episodes on YouTube.