Looking for advice on filling a gap between wall and sink

My husband and I remodeled our kitchen, and installed a vintage stainless steel sink.



The problem is, the wall isn't straight, so the sink meets the wall at the far right of the backsplash lip, then gradually pulls away to 3/4" at the far left. The cabinets that the sink sits on do the same thing, so it's not really possible to shove the left side closer to close the gap.

Husband wants to caulk it, but the caulking he's done isn't really good.

Any ideas for fillers - preferably paintable so we can match it to the wall paint?