Using a spare heat-block and some existing 3d printed parts with double sided tape, I threw together a test load platform. If everything goes well, I should be able to have the first loop running with a CPU cooler fan on a heatsink cooling the peltiers and pump the cool-side water to this little thing (drink cooler or more peltiers for cloud chamber?)

I did notice that the flow rate dropped even lower. Turns out that the pump I'm using is not what I ordered and is, in fact, a quarter of the power of the intended model (plate confirms this). It's clearly struggling to keep up with the flow resistance.
The good news is the higher power model is the same form factor, but the bad news is I'll be spending more money and that the pressures will be higher than what they are now.