The answer came from my friend and fellow-researcher Johan van Wieren:
"Those 2 mics to me look like the same 2 mics they used at the Saville Theatre 4 June shows. The shirt would make no sense in that case. But I read on Lifelines that they rehearsed at the Saville on June 1 and 2. One of those days, perhaps?"
Yes, Johan, that makes sense... The microphones match the ones used on 4 June, even the position they are used is the same. The shirt Jimi is wearing is an orange shirt which he wore up until the end of May. I agree with Johan: this photo [no other known of this session to exist] might very well be from either 1 or 2 June, taken during the Saville rehearsals. It was common practice to have photos taken during rehearsals at the Saville, rather than during the live show.
For the sake of completeness, this is the front cover of the album in question:
Jimi Hendrix Live - The Birth Of Success
Hor-zu Issue Germany vinyl LP album (LP record)
1. Driving South
2. I'm A Man
3. On The Killin Floor
4. California Night
5. Ain't That Peculiar
6. What I'd Say
7. Bright Lights Big City
With special thanks to Johan van Wieren.