I would look into overseeding with some grass species that take high traffic well, things like Bermuda are very high traffic durable.
Look for species that will be green in each season and plant all of them, that way you won't have an all brown space at any time of the year.
The biggest issue you will have is compaction, so for those "trails" that the heavy vehicles take you might need to invest in some sort of "paving" but it might not be necessary by now, since it seems you have been operating this place for a while already.
By the way, there is nothing more "sustainable" than grasses.
Gravel and wood chips (or anything you spread on the surface that is loose for that matter) will eventually spread out and will need to be raked back into place frequently, not very
energy efficient in terms of labor for maintenance.
All of those types of items will also become beaten into the soil, that means they will stabilize the ground as it becomes more compacted but this will be a
bear to de-compact
should you ever want to do so.
These materials also make it harder for
water to soak in, ever. Grasses will come up through both gravel and wood chips knitting the rock into an invisible layer (I have an area like this on my property that used to be a parking area, I am always raking up rocks).