How should I eliminate gaps in wood-grain miter joints?
I would probably use the same stuff you use to fill gaps in other laminate products.  I don't know how well it will hold up on the edge of a stair (in terms of working its way out of the gaps over time), but it'll at least blend in with the floor.  That stuff is made by a few companies in many colors to match a variety of laminates.  Should be available at your local big box hardware store.

For anyone in the dark about the Cap-A-Tread product, it's a laminate product designed to go over existing stair treads.  Kind of like the granite countertop systems that just lay on top of existing laminate countertops.  Looks like this:



It can also be ordered with a mitered edge piece that covers up the exposed stair end in the case of an open stair end, as OP is describing.  Basically a one-piece alternative to plank-and-bullnose for laminate on stairs.