Not a pedestal mount but rather a low cost solution for a center-mounted stick. No extension required (I didn't do it myself to avoid damaging the gimbal assembly).
It's just a regular wood board cut to size, I've used 2cm thick wood (about 1in). It's very solid and there's virtually no wobble.
You need a diameter of 11cm for the outer border of the base and the holes for the mount are on a 8,5cm diameter, spaced 90° apart
Then you just need some extended screws which fit in the WH base and voilà. (I found some laying around in my home). I could have designed a system for quick detach but I just screwed the board on the bottom of the chair taking care the screws are not too long to protrude into the cushion.
If I need to use the desk I just swap chairs as it's easier. I thought about doing the same with a metal sheet but I don't have any tools capable of those cuts and it's just easier to work with wood for me.
PS: for the throttle I've used one of those keyboard sliders with a board cut to size (in the pic it's slightly offset) but I'll probably go for a more solid solution since it's quite heavy and there's a bit of wobble.