Thsi can also in some cases be achieved by just re-seating the diaphragm and not tightening the pressure ring too tightly.
May the Lord bless you, Roddy! This is precisely what worked for me.
Now I suspect I may need to add some nail-polish to the screws to keep everything in place. (And possibly at a couple of spots on the ring to prevent it too from shifting?)
One thing: the three 'recessed' screw holes are in fact CLEAR holes which merely allow access to the screws beneath. These are NOT associated with the diaphragm position in any way.
So I kept the tone at the 'buzzy' frequency, (approx. 1.5kHz in this particular case) and loosened off the six tiny screws, including the two which hold on the wire end "sleeves", until they were all fully loose by about a quarter-turn. Then using a thumb and forefinger, I gently 'slid' the diaphragm around on the face, listening to the 'sharpness' of the buzz. After tuning for minimum 'fizz', I increased the amplitude slightly
and swept up and down. I found a slight 'fizz' at the low end (about 200Hz) and slipped the diaphragm around some more. I noticed however that the 'evenness of response' of the diaphragm 'singing' to the oscillator was already rather better, and this gave me some great encouragement.
So finally I took it over to the test preamp and... Hallelujah!!! Deep, stentorian bass!
[sniff] -I love this place!!! [sniff]