HE/TMR controller with paddles configurable in Steam

I currently have a Steam Controller. I'm after a replacement that has 2 sticks rather than 1 and a touchpad, as I find the touchpad difficult to use as a stick. However, I'd like to keep certain features of the controller, most importantly that the back paddles are separately bindable in the Steam Controller Configurator. Unfortunately most controller reviews I've found don't mention that - they'll talk about what you can do with the proprietary software, but not what Steam sees. I am aware that _games_ may not support new unique inputs; I just want to be able to assign things to them in Steam (e.g. multi-press macros).

It's not strictly essential, but I am hoping for physically large paddles, similar to the Steam Controller or, say, a real gear shift paddle. I don't really want fiddly little buttons. My fine motor control is suitable for reflex smashing the paddle, not hunting for a specific single-finger press.

Gyro and wireless support are not important to me, I never use them.

Currently the Dualsense Edge is a strong contender on features, but in order to get HE/TMR sticks (and any colour scheme other than white) you have to get custom parts, and that's...expensive.

If no such controller exists then so be it, I guess we'll see what Gamesir's alleged new SteamInput controller looks like.

Budget: £200 absolute max but ideally less

Country: UK

Platform: PC

Features: HE/TMR sticks, unique paddle inputs, analogue triggers

Games: driving and flight

Considered: Scuf Valor Pro (unknown paddle support), Razer Wolverine V3 Pro (paddles reportedly not supported in Steam), Dualsense Edge custom (f'ing expensive)