Fair enough. And no, DO NOT CHUCK PARTS. As your build will be unique it will be very worthwhile and although this is not a divergence competition, the performance will be interesting to follow. My suggestions were not intended to divert you. I suppose I miss interpreted your OP to be a review of the potential components of the design, I didn't release you had already acquired many of the components and were a lot further along.
OK. Regarding the base plate, your CAD image shows the diode mounts and the flex mounts recessed into milled depressions in the plate. It looks cool, but I believe that this may actually make the task of adjusting the mounts a little more difficult as well as significantly reducing the bending modulus of the plate. As you tighten the plate down against the TECs it will flex. The less it flexes the better both optically and as it effects TEC contact, thermally.
You haven't described your intentions for the cooling. Do you plan to cool aggressively below ambient? If so, do you have any experiments showing the effect on these diodes and how will you house the assembly to prevent condensation? Have you some idea of the TEC power requirements and will there be some consideration for the heat removal from the main projector base plate? I can make some suggestions.