It shouldn't be too difficult to use a trombe wall with pipes or something similar to replace the active fans. You could probably even run the intake pipes across the bottom of the trombe wall with a slight uphill pitch to preheat the air, go through the mass, and then vertical through the trombe wall to create a draft. Something like an Arduino could power flaps or valves to cut off air flow and be very power efficient.
I don't think adding metal is going to be very effective or economical as the mass is already fairly conductive. There is only a small temperature difference using outside air comparatively to burning wood in a RMH, so squeezing 1 or 2 degrees extra out of a
given amount of air will be difficult and probably expensive. Adding more than one pipe would greatly increase efficiency. The thing about a large thermal mass is the surface to volume ratio. If the mass is more circular or square it won't give off heat as fast as one that is really long and wide and thin at roughly the same volume. Adding surface area in the form of more pipes will give more contact for the air to dump heat in to the mass. One could be the regular RMH system for supplemental heat and another one or more for airflow only.
For a greenhouse, you probably wouldn't want a low bench, but rather something closer to square in cross section and closer to a more normal working height to serve as a work/plant space or perhaps with 'steps' for different tiers to hold plants. This would give off heat a bit more slowly but also take longer to lose heat. Given the soil all of the plants use then a full greenhouse would have much more thermal mass than many typical modern homes. The temperature swings shouldn't be drastic, so the mass won't need to be shaped to give off that much heat. In an emergency, the bell of the RMH can provide fast heat, but most of the time the mass should be sufficient if designed right. Getting the vents to open and close at the right times will be key to this.
I have been looking into this idea from the opposite perspective; I want a cool mass to moderate the hottest temperatures of my climate. Instead of preheating pipes with a trombe wall, I would use geothermal cooling. I want to take the night air and cool it further with subterranean pipes to then pull heat from a large mass. The idea of the mass and pipes is identical. Having a large monolith that isn't too thin in any direction and enough pipe surface area should be able to accomplish our goals.
Van Powell on YouTube has a lot of interesting videos, including making a greenhouse with a rocket mass heater. It isn't terrible large and doesn't have the system you are looking to implement, but there are a few ideas there that could be useful. You can insulate the north side of the building to retain heat, or maybe use charcoal to darken the surface of the mass in spring/fall to absorb heat from the sun. Hopefully some of these ideas will help you out.