Park tells you not to use the TB-2 tire boot as a permanent fix. I tried it anyway, on a similar slit that wasn't really bulging, but looked like it could get worse.

The edge of the stiff tire boot cut through my tube after a few weeks. oops.

Yeah, I'd try a tyvek patch, and watch the cut. If it starts bulging out, I'd throw out the tire. (I almost always end up throwing it out as the cut gets worse.)

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Permanent patches
On yet another cut tire thread, there was a post about gluing strong sailcloth inside the tire with contact cement. The cloth patch reached all the way across to both beads.

This seems like the only feasible fix, since it reinforces the tire all the way across, to resist the large forces from the air pressure.

I only get cuts like these once every 3 to 5 years, so I haven't felt like trying it.

I linked to it here.