The ideal space-filling "core" of a rete mirabile recuperator is (I argue) a checkerboard, with black and white squares flowing in the opposite direction.† This makes all adjacent channels opposite polarity (unlike a honeycomb) for maximum heat transfer, and also reduces internal drag and manufacturing complexity (unlike triangles). Mass manufacturing can be done via extrusion, or by gluing together 90° corrugated sheets. If the core consumes 80% of the total system volume this reduces 3D printing cost.
Trees typically branch 1-to-3, which is probably optimal because evolution. For an 54x54 grid that means 1458 endpoints, or 6.6 branchings. That's one 2-to-1 branching (common on the first "trunk" branch of a tree) followed by six 3-to-1 branchings, for seven total branchings. This is a typical value for a real biological tree, so we're probably moving in the right direction re:biomimicry.
In real biological trees the fluid flow slows as the branches get smaller, so it's probably good to emulate that.
† arguably a honeycomb shell-and-tube is more efficient geometrically, but it's non-symmetric and (more important) the manufacturing and rigidity/robustness is questionable
Aside: paraffin wax is used in actuators, e.g. automatic green house window openers, on account of its impressive expansion. The MVHR I have also uses it for automatic "summer" bypass of the heat recovery path.
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