Reporting back:
I re-assessed and it really was only the second octave E that needed me to do more work with my tongue to avoid it sounding like the side octave key wasn't doing its job. I followed Colin's advice above and ensured the side octave pip was clean which it seemed to be - the instrument is in pretty good condition. I tried an experiment where I used the palm key F (or alt-F would do) to vent instead of the side octave key and this demonstrated a very clear E (when opened the correct amount). So, it looks like if I was keen and confident (reckless?), perhaps widening the side octave pip hole diameter would make a difference, but there is no way I am going to experiment with that 🙂. So, I think this "weakness" of the second octave E is something the regular player of the instrument could deal with and highlights that perhaps my usual tongue position is fine for my own instruments, but may be a little too forward / low for this particular instrument design (the positioning is very fractional of course).
Thanks for your interest and help!
Roy