The fascia has wiggle room to move up/down and side/side a little bit when you loosen the screws. A tiny bit. This can slightly reduce the gap. There's no way that I can see for you to cover the gap up completely without external manipulation.

Given a common mounting angle in a car and the direction of sunlight and interior lighting, for most people, the chasis may never be visible. Setup at home on a rack or desk may be very different. My suggestion is if you want to cover it up, as you mentioned, go with the electrical tape cut carefully, or mask the chasis and apply a thin strip of black paint. I'll leave it up to you to decide between a brush and a spray can. I'd choose a small brush though. :)

If you look at the way the handle is mounted to the outside of the chasis, you'll notice there isn't any way to adjust its vertical position - otherwise that would be a convenient way to remove the gap.

You can also make sure to ask whomever decides to make new custom fascias to purposely take the size difference into account and design the piece to cover the gap.

My couple of cents anyway.

Bruno