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.
If you don't object to a transparent substance in the bottom of the basin, you can use acrylic casting resin, aiming for a product which specifically advertises itself as clear, as some of the available casting resins are not.
Mixing the product per directions and pouring it into the basin with a bowl under the drain will allow you to place the exact amount, while the excess runs into the bowl. Ensure that the basin is perfectly level prior to the pour for what I hope is an obvious reason.
It's typical to subject casting resin to a pressure pot to remove bubbles, but that's not necessarily practical in this situation. A heat gun (preferred) or hair dryer will help to clear bubbles.
As a possible bonus, you can mix a small amount of glitter or similar decoration if you wish to add a different touch, although that's not consistent with the flower motif currently in place.
This may not be suited if you intend to use abrasive cleansers on the surface, but they can be polished out with appropriate abrasives and plenty of labor.
There is nothing you can do, except to put in another drain. You cannot tilt that bowl in any direction that will but the hole you have at the bottom, so there is no way to avoid the standing water without having an additional outlet.
Plugging the center hole will probably (as you suggest) result in something that does not look very good (unless you can perfectly match the color on the ceramic), so I think your best option is to introduce a smaller additional drain hole somewhere along the bottom of the trough. If you want it to be unobtrusive, the best place to put an addition hole is toward the front of the vessel (the side farthest from the tap), since a user will generally spend to most time looking toward the back side of the bowl, underneath the tap.
Unfortunately, if you want to be able to fill up the sink, you will need to have plugs for both holes.
You could make another little flat hole on just one side of the round plate and have a little plumb to converge from there in the main central plumbing, so as the main hole will got the direct water and the new small one just the remaining.
Obviously you'll need a little of inclination to get the water stream to the right direction.
Just an idea.
If you have a shop press that's rated for at least a few tons, you can try reshaping the bottom of the bowl so that it is concave, instead of convex, from how it is right now. To do this right, you'll probably need to heat up the bowl so that it's easier to work with, but the heat from a torch might damage the paint. Even a heat gun might damage the paint, and bending the bowl into a different shape could also destroy the paint.
Then again, I'm going to have to assume you put the ring depression around the hole and that didn't damage the paint, so you might be good to go. Also, if you put in that ring, you probably have the size of shop press to make this happen.
What you'll do is to find or make another heavy bowl or depression for this to sit in while you apply pressure from the top. You might want to use a large piece of rubber or a sandbag with a piece of steel on top to apply even pressure across the dome. The idea is to get the dome to pop out under the bowl or to press it into a different shape with a depression, instead of the raised bit you have. If it's only a 3-5mm, this shouldn't be too difficult, but if the dome does do a "tin can" kind of popping out the bottom, you might have all the pressure of your press released all at once, so strapping the bowl and other press items down would be a good idea.
To be honest, I haven't done anything like this myself, so I'd check to see if there are any tutorials or videos that might have a better way to make this attempt.
