IM delegates the rasterisation of EPS to Ghostscript. GS can't return CMYKA images. So if we want to retain the CMYK transparency, we need to tell GS to make an RGBA image, then convert that back to CMYKA. "+antialias" can be used, as you do, to tell GS not to antialias.
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convert -verbose -density 1200 -colorspace sRGB test01.eps -colorspace CMYK t.tiff
We can output the unique colours:
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convert -density 1200 -colorspace sRGB +antialias test02.eps -colorspace CMYK -unique-colors txt:
# ImageMagick pixel enumeration: 8,1,65535,cmyka
0,0: (0,0,0,0,65535) #0000000000000000FFFF cmyka(0,0,0,0,1)
1,0: (0,0,0,771,65535) #0000000000000303FFFF cmyka(0,0,0,3,1)
2,0: (0,7490,5617,56540,65535) #00001D4215F1DCDCFFFF cmyka(0%,11%,9%,86%,1)
3,0: (44887,43989,0,28013,65535) #AF57ABD500006D6DFFFF cmyka(68%,67%,0%,43%,1)
4,0: (0,5483,54308,1028,65535) #0000156BD4240404FFFF cmyka(0%,8%,83%,2%,1)
5,0: (0,17128,62928,20303,65535) #000042E8F5D04F4FFFFF cmyka(0%,26%,96%,31%,1)
6,0: (0,34192,61057,24158,65535) #00008590EE815E5EFFFF cmyka(0%,52%,93%,37%,1)
7,0: (0,0,0,0,0) #00000000000000000000 cmyka(0,0,0,0,0)
We have transparent white, cmyka(0,0,0,0,0). cmyka(0,0,0,3,1) is out of 255, so this is your cmyk(0,0,0,1) out of 100. We can make all colours that are within 1.5% of white into tranparent:
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convert -density 1200 -colorspace sRGB +antialias test02.eps -colorspace CMYK -fuzz 1.5% -transparent cmyk(0,0,0,3) t.tiff