Thermal Properties of Seasoned vs Anodized Aluminum?

A surface insulating layer (whether deliberate anodising, natural oxidation, or seasoning) will only really affect the heat flow through that layer from the bulk metal into the food on top. It won't affect the heat-spreading effect used for even cooking, and it won't affect the heat capacity.

So now we're considering the difference between various surface layers. These will probably have a similar thermal conductivity to a ceramic pizza stone (to order-of-magnitude precision), but being thin layers between the food and the aluminium sheet heat reservoir will have a small effect compared to the temperature drop between the core of a pizza stone and the food on its surface. This means whatever has happened to the surface you'll couple the heat from the sheet to the food better than with a pizza stone, which would appear to be your goal.

The thermal conductivity of most foods that you'd cook on a stone/steel will be far lower - most consist of dough with gas bubbles in, basically insulating foam. That's what will limit the time for the middle to cook through. Perhaps a smoother layer will give better contact, but clean seasoning and anodising are both quite smooth.

More of an issue than thermal effects will be sticking. This is an application where you really don't want the food to stick, as it will carry on cooking while you free it up. It will also be a pain to deal with as I find with my home made aluminium pizza peel on thin bases. Hopefully the thorough, fast cooking will avoid sticking in the first place, but spills of sauce etc. will still need to be cleaned up, so a bigger question than heat flow would be ease of cleaning.