Try suggestions made in the following KB
Disabling that trigger will certainly avoid getting that error when versioning SDO_Geometry feature classes or creating multi-versioned views on feature classes that were versioned in previous releases. I'm not sure how Oracle would feel about having one of their triggers disabled though....
In this case I will be very surprised if this helps as danarng said that they were using SDE.ST_GEOMETRY. So metadata isn't stored in the SDO_GEOM_METADATA views.
It kind of sounds like there is a problem with the type when the SYS_TYPE function is called, so maybe having two dump files would actually solve the problem. If I were you I would open an incident with ESRI technical support.
Something else that you could try, if you haven't already, is dropping the table indexes and disassociating any stats before you export the data. As for giving exp or imp a try, I think for ST_Geometry you have to use the expdp and impdp.
Finally, here is a KB article with a number links to other known issues with import/export of ST_Geometry: