SLA (Stereolithography) printing on the budget end of the market offers around 10cm x 10cm build area - which is fine for your use and very high resolution. The cured resin does not shrink and warp like the thermoplastics do so it is a lot easier to replicate and interface with those tight LEGO tolerances. Further more I think the resin cures into an extremely tough, and rigid plastic with just a little flex which is reminiscent of official lego.
I don't pretend to be an expert by any means... But I'm fairly sure what you're looking for starts at about $1200 USD for a Form1 clone or a $1500 for a XYZ Printing Nobel. If you happen to have a DLP projector laying around then you're in luck because there are sub-$1000 kits to turn it into a SLA printer.