Koji asked me to calculate the thermal resistance between the cold head and cold plate from Megastat cooldown data, to compare to the theoretical thermal resistance of the copper braid. This way we can determine if cold plate cooling is limited by the braid itself or by the contact(s) between the braid and cold head / cold plate.
After folding the copper braid in half, its cross-sectional area is 1.34e-4 m2 (source here) and I estimated its length to be 30 cm. I used a room-temperature value for the thermal conductivity of copper, for simplicity (~400 W/m*K). The "theoretical" thermal resistance of the copper braid should therefore be 5.57 K/W.
I used existing cooldown data from the cold head and cold plate to fit the thermal resistance between the two. I ignored effects from room temperature and simply modeled conductive cooling from the cold head to the cold plate. The result of the fit was a thermal resistance of 5.75 K/W, obtained from data. This value is pretty consistent with the calculation above, implying that the cold plate cooling is hitting the physical limits of the copper braid.
If the copper strap were instead a solid bar with the same nominal diameter (0.483"), the thermal resistance would drop to 3.15 K/W (a factor of 0.57 in cooldown time).