OP, one other thought is to look into RTA (ready to assemble) cabinets from another company. The shipping can be expensive, so I would look for somewhere nearby and figure out how much shipping would be before going this route. Scherr, Barker, Semihandmade - there are a lot out there nowadays. Even Home Depot has some on their website (finished already, though, I think).
This could be another way to get an unfinished cabinet that you could paint.
The Ikea bath cabinet would likely be the cheapest/easiest choice if you like their sink and want to use it. Their stuff is all engineered to play well together.
Are you familiar with Houzz (formerly Gardenweb)? It's like the BBB of home projects....
https://www.houzz.com/discussions/41...ikea-vanities/