Thank you both for the replies.
In your use case probably you will get better bang for the buck using some post production tool such as iZotope's RX which can be purchased at a discount now and then.
I agree that it makes sense to deal with the noise in post, which would give me more control over the end result. I need to lean how to use the software I have - I note that two products I own have noise reduction plugins!
I think where I struggle is with dealing with wide spectrum variable noise. So noise form individual cars, aircraft (I live not too far from Heathrow!) etc. I was hoping that NoiseAssist may be something clever, that monitoring these variable noises and cancelled them out. SoundDevices are yet to come back, but I will confirm their response when they reply. I think most plugin are good at reducing consistent noise, so perhaps the general rumble from a distant road, but if you are aware if iZotope's RX can deal with variable noise levels I would be interested to know.
Your random mic does record a little of your object, but everything which is around and is unwanted noise. Because its recorded phase reversed it wil cancel out the the same signals in the recording of the object when added in the mix.
Never thought about doing this, but have seen phase inversion used to demonstrate the difference in noise floor between a 16 and 24 bit recording - not a lot if you have a reasonable signal to noise ratio in the first place. I have also thought about using phase inversion to check my edits - basically that I have only deleted noise rather than bird vocals.
I think I will give your suggestion a go as an experiment. I think that doing the phase inversion in post may be best, particularly as I think there will be a lot of fussing with levels (after all you are trying to match a sensitive direction mic, which should reject some off axis noise, with the noise picked up from a less sensitive one, but probably picking up noise from a wider area).
I think it would probably work best with a shotgun, so you have two mics with a flat frequency response - with a parabola, I think you would need to add equaliser effects to the noise channel, to counteract the fact that higher frequency sounds have greater gain in the parabola . Perhaps overthinking it - and an experiment wouldn't be that hard to do in any case.
I only have a cardiodal mic to use to record the noise and suppose an omni would be best, but I think it could work - with traffic noise set up the mics as close as possible with the directional mic facing away from the noise and the cardinal facing towards it; for aircraft noise, perhaps face the cardiodal mic upwards.
Not very portable, but it could be a blast on occasions, if it it works well - we have some Nightingales nearby, but unfortunately the place borders a main road - an ideal test case!