Now I'm starting to understand the problem! What I'm getting is that you are carving or cutting stone, which leaves a rough surface with tiny edges of crystals jutting out of the matrix. You would like to smooth this surface back to the nice glassy surface you would get if your fractured a single CaCO3 crystal along one of it's fracture planes. One way to accomplish this is simply to use abrasives that will wear down the edges of the crystals to form a smooth surface, but you are doing it chemically using water and an acid that will dissolve the crystals and reform them, preferably dissolving the high edges and reforming them in the valleys, making a smooth surface. Is this more or less accurate?
Unfortunately, it is not the chemical speed of the reaction that will be your problem, and increasing the rate of the reaction chemically is almost impossible. Acid-base reactions are among the fastest reactions we know. The problem is the physical speed at which you can bring the stone into contact with the acid. The stone will react only where it is in contact with the acid solution, so your reaction is only occurring in a molecular layer at the surface of each crystal. If you have crystal edges and valleys differing in height by even a couple of millimeters, that will appear to be a very rough surface, but it contains a lot of molecular layers to work your way through. I presume that your oxalic acid mixture is already totally saturated with calcium carbonate so you are depositing calcium carbonate in the valleys as fast as you are dissolving it on the peaks, but it will still take some time to expose and dissolve all the peaks.
There are some ways to increase the fracture rate on the surface and grind some more of the peaks off, which may add a physical component to your chemical reaction and speed things up some. Possibly heat, vibration, rapid light hammering, ultrasonic conditions, the addition of abrasives or using more even particles of calcium carbonate in your calcium carbonate/calcium oxalate polishing mixture. You might also consider spraying the warmed surface with a calcium carbonate solution so the water will evaporate and fill in some of the valleys before the oxalic acid treatment.
The dark spots are probably due either to very large crystals or to impurities in the surface. If there are silicates or aluminates in your marble, it may be coming up in your solution and leading to dark spots later in the process. I suspect the larger crystals though, since you see the dark spots as you speed up the process. In a slower process, the crystal faces would be etched by the oxalic acid solution adn wouldn't appear as dark.
This sounds like a very interesting process to me - please keep us informed as you experiment.