Jeremy my concern is the leverage from any side load the arbor would receive (wind? other?). This would anchor the post to the foundation but likely will act as a hinge unless the above/below grade steel is significant - setting light posts (very little wind load) we used 18" bolts tied to rebar in a 4' hole - then the pole is continuous aluminum. In your case the DF will sink/swell with humidity so the steel socket is all that will keep it vertical (your left over DF posts are dry, but mine are a year drier and still shrinking).
If you are confident that the location will not see significant loading (I don't know how to measure that) Connecticut Post and Beam make some AL joints (instead of true timber frame mortise/tenon) including post base - the plate fits into a slot in the post so it is not highly visible - might be an option for something similar to what Eddie was recommending to get a solid connection to the concrete foundation along with a significant connection up into the post to reduce the hinge leverage. Not sure if AL or steel is better in this application, but AL may weather better?