How can I get water to drain out of a sink where the drain opening is higher than the bowl bottom?

First off I screwed up where I drilled the hole for the drain. The middle of the bowl is actually raised so the water pools in a circle around the drain:

I'm curious what my options are now… Is there any way I can salvage this? There's about 3-4mm of standing water in a ring around the bowl.

Could I put another smaller drain in back of the bowl? I'm wondering if I could even plug the hole I drilled and not have it look awful.