Best machine for cutting packaging foam for a small business?

Hello all.

I run a small business on the side that sells motorized astrophotography mounts. Cutting our product's packaging foam by hand is a pain (and quality is inconsistent between techs), but ordering custom-cut foam is too expensive. I'm a mechanical engineer by day and have broad (albeit mostly shallow) experience with various cutting methods, but I am a bit stumped as to whether laser, waterjet or hotwire is the right fit here. Laser seems to be too expensive, requires a lot of tuning, and doesn't do well with deep cuts, not to mention ventilation and safety systems are a must. Waterjet is pricey and messy. I'm leaning towards a two-axis CNC router/hotwire machine. I'm looking at cutting ~1000 pieces of foam per year. My preliminary budget is $2k. Not afraid of the DIY route if it's the best option.

Does anyone have professional experience in this arena? What kind of machine would be the right fit here? Specific model suggestions would be the icing on the cake
 
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