Once the thermal mass of the "batch" of air is relatively small compared to the thermal mass of the regenerator, adding more thermal mass doesn't help.
The reason you can't go to town with high surface area is viscous drag. The fans make a lot of noise when they have to work at high speed, which they have to do to produce higher pressures. Fan blade noise increases in proportion to the eigth power of blade velocity. So really really fast. So if you make the holes in the regenerator smaller and the walls thinner to increase surface area, you don't get enough flow.
The usual units really hobble at the best of times. If you calculate how much energy (which increases linearly with flow*efficiency) they save a year, they usually actually cost more in amortized total cost of ownership than they save.
The best thing is to redesign both the fan and regenerator, that's what I did.
There is a nice fan that's produced by a german company that I'm trying to get samples of but they are super slow.
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
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.