CMYK won't do it for this design.
1. CMYK on white shirts can look pretty good, on black, not so good.
2. You will most likely lose too much detail because you are using only CMYK and your entire design would rely solely on halftoning.
3. Spot colors would look the best for screen printing, but it looks like there would be 14 colors, so I don't think that would work.
4. You could have spot process which would reduce the colors down to 8 or 9 and it would look pretty good. There would be halftones, but not like CMYK. The Red and Yellow mixed would make orange. So this reduces the screens, but with spot process, it's usually 8 or 9 colors to get a very good representation.
5. Transfers would still be pretty expensive because most likely you would need screen printed ones. If this is the case, you might as well invest in screen printing.
6. DTG most likely wouldn't work because of the size of the print and the volume of ink that would be needed. These would be very expensive shirts.
What I would do is look for a high end screen printer. Some require a minimum of 144 and other 288, but either way, this IMO is a spot process printing job. It would be a good quality print at a better price than spot colors.
As a side note, you could probably have this printed as a 6 color design with halftones, but it most likely wouldn't look as good as an 8 or 9 color design. If you go this route, it still could look good with a fine enough halftone, but your colors would be a little off. White, Red, Blue, Green, Yellow, Brown. You would use the black of the shirt obviously for black and these other colors would either be shaded or mixed to get the various colors or tones. With a good screen printer, they should be able to pull it off with great results.