With the one inch reference you've provided, I would suggest that you consider to use a CNC router of sufficient size. Your requirements of a smooth finish would mean substantial post-processing (sanding) of the 3D printed part, while many CNC routers have the ability to perform very smooth surfacing action as the final pass of the cutting bit.

Additionally, you may find it useful to perform the cutting process with a CNC router to create your wax master directly.

Your budget would allow for a suitable sized CNC router with quite a bit left over. You can get an OpenBuilds OX kit that will do 12" x 18" for less than a quarter of your proposed budget. Larger models are more expensive and more capable, of course. Fully assembled CNC routers will be more expensive, of course, but you miss the fun of assembly, depending on your point of view.