Is there a good way I can work this into the design at this stage without
going to the lengths of using some sort of mixer system?

Nah. Put it a mixer system. You need fine specific temperature control for
that application. You might get away with putting the mixer (and pump) near
the heat bank (presumably in some sort of airing cupboard), rather than
trying to find space near the floor in question, although with all these
circuits, pumps, valves etc., it's going to look like the engines of the
space shuttle before long. Make sure you document what all the bits do!

Christian.