It's not going to be easy to use a different cockpit unless you get lucky and it happens to fit their proprietary spacers. Even with their own cockpit, it looks like you're forced to use one or two of those oddly angled spacers.
If you want to use a different setup, you'll likely need to design your own bearing cover and possibly your own angled spacers as well.
I really don't see the point of such a proprietary design, especially since the cockpit and headset aren't particularly special. I could understand it if the cockpit sat flush with the top tube for a seamless transition, but it doesn't. Instead, it looks more like a makeshift workaround.
If I had to guess, they probably originally designed the headset for a completely different cockpit (similar to the Ridley Noah Fast 3). But they must have messed it up and attempted to fix it with these awkward spacers to make it work with their standard cockpit.
