Here's my simple hack. I'm lucky that the chair arms were simply bolted on, so it was easy to mark the holes on some 20mm ply, then make up the sides to a rough shape, they aren't in the final shape yet as I think they need some finessing so they don't look like slabs of plywood bolted onto the chair.... I clamped the actual joystick controllers to the new sides and placed them where I thought would be most comfortable with height and angle, marked up where the bottoms would need to be and made the supports to suit. They are both angled down as I sit with the chair reclined when gaming.
I then worked out the best size for the support platforms and added extra support brackets underneath from more ply.
On the left side one (as you look at it) you can see a small stop end plate, which is there to prevent a mouse slipping off the mat when I'm not using the joysticks.
on the underside of the left one at the back there's hooks screwed in to hang my headset and it's separate volume controller.
I also plan to add USB sockets using extention cables to the seat so that I can plug peripherals directly into it, increasing the amount of cable distance I can have, as currently it's a bit tight.
Another plan is possibly to add a keyboard support too, so I can still type without having to sit forward with the KB still on the desk - whether this will be a desk extention platform or built onto the chair I dunno yet.
So far I'm very pleased with it and wish I'd done it years ago, as sitting right forward with joystick and controller on the desk wasn't optimal, and was prone to make my wrists ache.
I've been wondering about how to decorate it though. I was thinking of metal plates, possibly riveted for the sides (using salvaged soda cans) sort of aircraft style, black for the side supports etc, but your idea of granite grey pleather sounds really good, and the whole thing could do with a refurb; the foam in the seat area is mostly flat now, and I'd already bought some to renew it.
(excuse the terrible mess in the back - those are some other woodwork projects (plus my modelling desk) and with winter now coming they all need to come indoors, so they are not affected by the damp air).