There are places online that sell unfinished doors/drawer fronts. I remember someone with cabinets similar to yours posting about getting them.
You would have to strip the lacquer off off your cabinets and sand them before staining, but it shouldn't be difficult to get the doors to match if you get the same type of wood.
I agree with getting new doors. I think Home Depot maybe even offers this. But you might have to go with a painted finish (or buy unfinished then paint yourself) to match a new door front to the bases. I like your dark counters! Maybe a color like grey-green would look good with that!