How To Cut/Shave Existing Drop In Sink To Fit New Faucets
What is the material of the drop-in sinks? If it is porcelain on cast iron grinding would expose cast iron which would rust. I suppose you could paint it, but this probably would rust through. If the sinks are solid ceramic you might be able to grind it away with a diamond wheel on an angle grinder or diamond bit on a high speed rotary tool.

I think it would be easier to cut off parts of the flanges on the new faucets. Would you have to cut off parts on both sides of the flanges? If you could confine the cutting to one side (the back), then it would be against the back-splash and would not visible. Of course you want to leave enough flange to seal.