Centring mechanism? What centring mechanism?
There isn't much to see in fairness. I have put cable ties tightly around the centre spring coils for the original centring mechanism to just keep it out of the way (if I could be bothered I would remove the spring and plate altogether). After that the big springs that you see coming from the sides provide as much of a centring mechanism as there is. It's a very fluid feeling.
If you let go of the stick it does centre but in a fairly laid back fashion - there is no twang to a strongly defined centre point. The only time this causes a minor problem is in Black Shark where you have to centre the stick after trimming but, in fairness, it's easy to overcome and will generally naturally return to close enough to centre to give you back control.
The key to getting the stick to centre effectively was to use pull-springs that are almost entirely relaxed when the stick is centred then make it so that they can slide freely through the eyelets on the right-angle plates at the edge of the body of the stick when the stick moves towards them. The sequence of parts from the shaft is: cable-tie holding the ends of the springs > spring > drinking straw > eyelet > wing nut > retaining ring.
The drinking straw is probably not necessary but it prevents the spring going clonk, clonk, clonk as you move the stick and helps the spring get out of the way when the stick is at extremes of its movement.
The hardest thing about this will probably be to find the right spring. The ones I used came in a pack of assorted springs I got from Halfords. They are 2.25" long and really powerful - far more powerful than I thought would be of any use. I just went through the box trying each likely candidate until I found one that works.
Anyway, here is a close up: