Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
This is a rare occasion where using a transparent black to overprint the light colors to make the darker shades could work for both the front and back.Hybrid would be a good option as well if you could outsource, but if you wanted to do this in house without heat pressing or direct to garment 400 times then here is how this could be done if there is flexibility in not getting the exact colors, but also no halftones so it will look great, just not the exact same. Some concessions should be able to be made to make a great product.Also, Royal Blue doesn't discharge well so I would push the client towards the Aqua shirts.Here is how this could be done, and since you have a 12 color press you'd need to go around twice (gasp) unless you could cut like the orange out, and put a flash there.Back 1 ) White Base (may not need to base most colors on Aqua blue)2 ) Flash (or inline heat press)3 ) Black (under prints light pink to make dark pink)4 ) Mid Blue5 ) Skin Tone6 ) Mid Red7 ) Light Pink8 ) Light Green9 ) Orange10 ) White11 ) Transparent Black - like .01% black pigment in clear base with matte additive (overprints to make darker shades of Blue, Skin Tone, Red, Pink, Green, Grey)12 ) Transparent White - like .02% black pigment in clear base with matte additive (overprints Light Red, and Light Blue to make lighter Shades)Rotation OneWhite Base, Flash, Black (thin ink on no base should be fine with no cool down), Mid Blue, Skin Tone, Mid Red, Light Pink, Light Green, Orange, WhiteRotation TwoFlash, Transparent Black, Transparent WhiteThe front can be done in the same method as above.This result will get you all solid colors, it could also be done using simulated color process in one rotation but same thing is that some colors will likely shift and you may still have to go around twice.Like Brandon said, sub it out, or do hybrid transfer or DTF / DTG, but if you wanted to push yourself and do some real time R&D this can be done the way I said above. If you do it post results, and if you send me the file for the back I can show you how I'd set it up in illustrator, basically just take the darker shades, and add it to the light, and then the dark shade becomes a overprint layer.Good luck and report back!