It should be a procedure which is controlled and has an element of VMC and IMC built in.
anything less than an IMC procedure built in is asking for trouble because you cannot be assured of good VMC in reality
Pace,
A good reason for conducting a Precautionary Landing would be if a pilot was completely lost (especially with night and or bad weather approaching)
If, as you suggest, they are already completely in it " in rain 1000 meter vis or less and down at 250 agl with bits of cloud passing under the aircraft" I would call this a Forced Landing (due Wx) with power available to adjust the approach.
mary,
A "constant aspect approach" would involve flying a curve from downwind to just above the "threshold" - I am not sure a "diagonal" comes in to it.
Generally, I would suggest, some timing does come in to it (ie 10 seconds from the downwind point to commencing the curve) in order to more easily place the aircraft at 100' to 200' on short final (particularly with high wing aircraft) to give time for small adjustments to the last part of the approach before landing.