I'm afraid I'm not contributing very much in the way of viable candidates, but this is a very educational research project!
For instance, I did not know that the Shadows (Cliff Richard's backing group) had a Eurovision entry without him, or that they actually sang - all their work I've heard without Cliff has been instrumental. They came 2nd in 1975.
I also didn't know that Liz Mitchell, before she was in Boney M was in the Les Humphries Singers who represented Germany in 1976, placing 15th!
I knew about Brotherhood of Man (1976 winners) and I probably should have known about The New Seekers (2nd in 1972) - I've indexed both bands in bandspace but haven't checked each member for their profile status yet.
Spanish duo Baccara, best known for "Yes Sir, I Can Boogie" finished 7th in the 1978 competition with "Parlez vous Francais", obviously representing who else, but Luxembourg.
Hah! I keep getting videos on Youtube for Dschinghis Khan by Dschinghis Khan, I didn't realise it was an actual Eurovision entry! (Germany, 4th, 1979)
Prima Donna, the band performing UK's 1980 entry aren't that well known but two of their members were Kate Robbins (of Spitting Image, Eurotrash) and Sally Ann Triplett who was also on TV a lot. I doubt they have profiles, both are living.
I'm sure I don't need to mention Buck's Fizz. I will mention Nicole Seibert (living), who won in 1982 with Ein Bisschen Freiden (which we translated as A Little Love), a particularly lovely song.
I don't really recognise even the British entries from about 1983-1992, though a few finished top 5. Samantha Janus (better known as an actress) had a go one year, and Sonia's 1993 hit Better The Devil You Know which finished runner up has probably been overshadowed by a Kylie song with the same name. Aussie Gina G with Ooh Aah Just A Little Bit in 1996 surprisingly came 8th, that one still gets play on the music channels! Then in 1997 Katrina and the Waves won it.
Anyway, there have been some great suggestions elsewhere, I don't think you'll have a problem finding a full roster. I'll see if I can connect some people up anyway.