Epson has a number of black projectors. The 4050, from what I can tell, is the black version of the 4010.
https://epson.com/For-Home/Projecto...Advanced-3-Chip-Design-and-HDR/p/V11H932120MB
But, here are the rest...
https://epson.com/For-Home/Projectors/Pro-Cinema/c/h320
Really, the LS10000, 6040, and 4050 are the ones to look at. The 4040 is based on the 4000 from what I can tell.
If you are looking at the LS10000, then you should be looking at a JVC or Sony instead.
I did mention the AVS classifieds. While I hate sending people off site, they have things pop up and get sold VERY quickly at reasonable prices.
https://www.avsforum.com/forum/252-front-projector/
Right at the top is a Sony 285ES for $3,000. Another one brand new for $3,100. People with more money than myself, like to upgrade their projectors every year or two. Makes for some great deals!
https://www.avsforum.com/forum/252-front-projector/3034358-sony-vpl-vw285es-4k-projector-3000-a.html
Everything is budget dependent, but I would try to find the extra cash if I could figure it out. I realize $2000 vs $3000 is a solid 50% difference.