Two things are throwing me about your descriptions. First the shrill call. No way does a Nightjar have a shrill call. It is a churr and very unmistakable. This is done when perched.
Also there is a one note, fairly quiet, given mainly in flight but also just before take-off, primarily by ♂. Alarm- and warning-calls consist of series of ‘chuk’ or ‘chek’ sounds, with some units doubled (i.e. ‘chek-ek’, etc.); not unlike ‘chink’ or ‘chik’ calls of Blackbird.
The other problem I have is your description of a darting flight. I can't recall Nightjar with that type of flight. Their flight I would loosely compare with a butterfly. Quite a clumsy flight.
I would also expect you to possibly hear their wing clapping as it is quite distinctive.
Having said that, if it isn't a Nightjar I'm not sure what else it could be.
Woodcocks fly at similar times but their Roding song of ♂ consists of (generally) 2–5 slow but accelerating deep croaking or growling sounds (snore-notes) followed by sudden loud shrill sneeze (sneeze-note), each complete sequence mechanically repeated with silent intervals of 2–2.5 s. ♀ may call down roding ♂ with softer version of ♂’s sneeze-note: ‘iiiitz-iiiitz’, ‘psit’, etc.
Now that I have confused you I will leave you to it.
John