Peltier modules are bidirectional.
Can you switch the water flow between heated and cold via valves, and reverse the peltier supply polarity for heating / cooling?
It would save the mass of the second set of peltier modules and allow the one set to be distributed more evenly under the bed.
If you used a second heating channel with an appropriate PTC (rather than the normal NTC) thermistor for the cooling control, the board would read the temperature in reverse and should allow it to drive the cooling control?
The displayed temperature would be wrong, but it should allow regulation?