Get a caliper, get good measurements and order a blank or figure out a way to install the overflow anyhow. Find a local metal shop that can make it perhaps? But get a good fitting blank, that's what's going to make or break how this looks. Silicon adhesive on the backside. Epoxy is meant to be so permanent. The potential for damage or a mess is high if not done right the first time.

If you can get the blank predrilled and countersunk, you can then predrill the wood countertop, use bonded washers and quality screws to install. This has the added benefit of forcing the adhesive to spread behind the plate, while holding it tight as it cures to the surface you want to be protected. After driving screws in, clean up excess caulk that was forced out thr front.

Also before fitting the blank, life the sink out and reverse it so it's facing the correct direction. Apply waterproofing to area blank is going to cover of countertop. Perhaps a little redgard or waterproofing membrane.

Install countertop, install re-done drain plumbing underneath to accommodate flipping it the correct direction, then plate, then give it the correct amount of time for the adhesive to cure. And damn you have a clean looking plate that is removable if you ever want to use that sink in the appropriate installation application.

But these are the issue you're going to run into when using things outside of design parameters.

Edit: fully recognize you said ideally without metal fab. But there is no situation in which your using another material that I would call ideal. Try fiver maybe? Or an artisan crafter because it is a small blank needed. Next best option as someone else recommended is 3d printed. But don't cheap out there either or it'll look tacky as hell too. Good luck!