What are appropriate techniques to ensure homogeneous solidification of an agar-based aqueous solution?
Let me suggest two avenues :

Vertical set up à la potter's wheel: At school we once did something related to your aim: using an old $\pu{75 rpm}$ record player, obviously no longer needed, with a beaker containing previously molten bees wax in the centre.  Under constant rotation (rather than the revolution by a centrifuge), the surface of the wax formed a nice meniscus which frooze by the slow cooling. While I am not aware if the alread-gel particles would keep nicely floating in your suspension, until all is solidified, it may be worth to giv it a try.  Centering of the whole ensemble is important (unbalance and spill), especially if the sample to be generated should really become as large as a human head.  Scaling up appears possible (larger beaker / bucket, and potter's wheel).

Horizontal set up: If you were interested in a smalller sample, a roller mixer would be an alternative:



(screen photo)

A wide mouth bottle (like the still cylindrical $\pu{1 L}$ polymer centrifuge bottles used in biochem) would be filled by immersion with liquid and -- still immersed in solution -- closed with the lid to ensure absence of air bubbles in the bottle.  After external cleaning of the bottle, they would be layed along the rolls.  Subsequently, you would turn on and crank up the rolling and hopefully the gel would form sooner than the liquid dropping out from the bottles.  (One may orient the bottles with the lids facing you, and place a bucket underneath them to collect potential spill.)  You may find such a roller mixer in biochem groups cultivating their own cell cultures.