If you could Jack it up to level and add pt 4.6 beams across the soil
tied to each corner post, that should stabilize it, no?
You could also dig a trench between each pait of posts and pour an
after the fact footer upon which to rest the horizontal support beams,
but I think the wood would do.
When we redid our home in Fl, the floor joists needed repair work and
my wife and I jacked up the back side of the addition with the jacks
from her Ford Aspire and my Pontiac Grand Am!
Another approach might be to dig eight holes just (2ft ?) outside the
perimeter at the corners, fill those with Concrete and use them to
support vertical (6x6 ?) members that would support horizontal (4x6)
members :"latticed" under the existing structure after it was leveled.
THen, add a "walk" (with railing) around the new perimeter as if
intended all along.
PS: Nice looking structure.