Bingo!

I have just determined that the strip of metal I used to mount the
sensor to the front of the engine has a resonant frequency (with the
sensor attached (of course)) around 95 HZ which is very close to the
frequency of the spike I was seeing.

I think that solves the mystery of the 3.5 crank vibration.

Many thanks to those who replied, I learnt something today!

Mark