hello Wodineye
From my perspective it seems like you have somewhat of a problem, sometimes they can be solved but not always easily
From the information you are giving us to use as a reply guide, I would say that you may have to resort to mechanical joint fasteners at each joint intersections just to be safe
I have used custom saddles fitted around the vertical post which project inward and along side the horizontal girt, it then is just a matter of drilling and fastening the custom saddle's arms with bolts through the girt
It appears to me that the frame was created very roughly especially at the intersecting points by whoever originally
That should make the frame strong at the critical points
Other than that I really don't know what to say maybe someone else will jump in with a better solution
NH
Richard