i think the solution to the viscous-drag problem is a fractal regenerator similar to a mammalian circulatory system, in which a branching tree of "artery" air passages feeds a set of "capillaries" distributed over a surface of high hausdorff-besicovitch dimension which separates the "arteries" from a second branching tree of "vein" air passages; this squares the circle of low air resistance (because the capillaries are short) with high heat flux (because the total surface area of the capillaries is large). if you have two counterflowing sets of capillaries instead of one, you have a
rete mirabile recuperator
obviously this structure is not feasible to manufacture by conventional processes, but you can 3-d print it
cf. https://dercuano.github.io/notes/capillary-heat-exchanger.ht...
it seems crazy to me that people would use alumina as a regenerative medium for house ventilation; it's a pain to get into the shape you want, which makes it expensive in practice even though it's an abundant natural mineral. it does have an immense virtue as a regenerative medium, which is that it can withstand like 1750°, but if part of your house is over 1000° you have bigger problems to worry about than the efficiency of your hvac system. if you're trying to maximize the thermal mass of a stable solid per dollar, something like unfired clay is probably optimal, though it expands and contracts with humidity; lime mortar (quicklime and sand) avoids that problem. those are low thermal mass per kg; to optimize that, you'd probably want polypropylene instead (or paraffin wax, but it might melt)
unfired clay has significant moisture-adsorbent ability too, which is why it expands and contracts with humidity. muriate of lime is commonly used as both a (deliquescent) desiccant and a flocculant for clay colloids used as ceramic glazes; i'm not sure to what extent clay with muriate of lime in it can function as a solid desiccant
but maybe i'm missing some basic knowledge here, so plausibly these are stupid ideas; wikipedia is no substitute for experience