Hi Panagiotis,
Thanks for the response and my apologies for the delay in responding. The '40020' article you provided set me on the right path, though as all the databases I currently had were in the same state. I ended up having to rebuild a DB from scratch and copy the objects back in using ESRI tools. Once I did that, the privilege issue was resolved.
For future reference for anyone else with this issue, the following objects were found to be granted to PUBLIC role after I rebuilt the database.
ALL_ST_GEOMETRY_COLUMNS_V DELETE
ALL_ST_GEOMETRY_COLUMNS_V INSERT
ALL_ST_GEOMETRY_COLUMNS_V SELECT
ALL_ST_GEOMETRY_COLUMNS_V UPDATE
ARCHIVE_UTIL EXECUTE
BLOB_ARRAY_TAB EXECUTE
BND_ROWID_TAB EXECUTE
COLUMN_REGISTRY SELECT
CONNECTION_ID_GENERATOR SELECT
DBTUNE SELECT
DBTUNE_UTIL EXECUTE
FLT_ARRAY_TAB EXECUTE
GDB_ITEMRELATIONSHIPS DELETE
GDB_ITEMRELATIONSHIPS INSERT
GDB_ITEMRELATIONSHIPS SELECT
GDB_ITEMRELATIONSHIPS UPDATE
GDB_ITEMRELATIONSHIPS_VW DELETE
GDB_ITEMRELATIONSHIPS_VW INSERT
GDB_ITEMRELATIONSHIPS_VW SELECT
GDB_ITEMRELATIONSHIPS_VW UPDATE
GDB_ITEMRELATIONSHIPTYPES DELETE
GDB_ITEMRELATIONSHIPTYPES INSERT
GDB_ITEMRELATIONSHIPTYPES SELECT
GDB_ITEMRELATIONSHIPTYPES UPDATE
GDB_ITEMS DELETE
GDB_ITEMS INSERT
GDB_ITEMS SELECT
GDB_ITEMS UPDATE
GDB_ITEMS_VW DELETE
GDB_ITEMS_VW INSERT
GDB_ITEMS_VW SELECT
GDB_ITEMS_VW UPDATE
GDB_ITEMTYPES DELETE
GDB_ITEMTYPES INSERT
GDB_ITEMTYPES SELECT
GDB_ITEMTYPES UPDATE
GDB_REPLICALOG DELETE
GDB_REPLICALOG INSERT
GDB_REPLICALOG SELECT
GDB_REPLICALOG UPDATE
GDB_TABLES_LAST_MODIFIED DELETE
GDB_TABLES_LAST_MODIFIED INSERT
GDB_TABLES_LAST_MODIFIED SELECT
GDB_TABLES_LAST_MODIFIED UPDATE
GDB_UTIL EXECUTE
GEOMETRY_COLUMNS SELECT
INSTANCES DELETE
INSTANCES INSERT
INSTANCES SELECT
INSTANCES UPDATE
INSTANCES_UTIL EXECUTE
INSTANCE_ID_GENERATOR SELECT
INT_ARRAY_TAB EXECUTE
KEYSET_UTIL EXECUTE
LAYERS SELECT
LAYERS_UTIL EXECUTE
LAYER_ID_GENERATOR SELECT
LAYER_LOCKS SELECT
LAYER_STATS_UTIL EXECUTE
LINEAGES_MODIFIED SELECT
LOCATORS SELECT
LOCATOR_ID_GENERATOR SELECT
LOCATOR_UTIL EXECUTE
LOCK_UTIL EXECUTE
LOGFILE_UTIL EXECUTE
METADATA SELECT
METADATA_ID_GENERATOR SELECT
METADATA_UTIL EXECUTE
MVTABLES_MODIFIED SELECT
OBJECT_LOCKS SELECT
PINFO_UTIL EXECUTE
PROCESS_INFORMATION SELECT
R4 SELECT
R5 SELECT
R6 SELECT
R7 SELECT
R8 SELECT
RASTERCOLUMNS_UTIL EXECUTE
RASTERCOLUMN_ID_GENERATOR SELECT
RASTER_COLUMNS SELECT
REGISTRY_UTIL EXECUTE
SDENUMTAB EXECUTE
SDEXMLTOTEXT EXECUTE
SDE_ARCHIVES SELECT
SDE_LAYER_STATS SELECT
SDE_LOGFILE_POOL SELECT
SDE_TABLES_MODIFIED SELECT
SDE_TABLES_MODIFIED UPDATE
SDE_UTIL EXECUTE
SDE_XML_COLUMNS SELECT
SDE_XML_DOC1 DELETE
SDE_XML_DOC1 INSERT
SDE_XML_DOC1 SELECT
SDE_XML_DOC1 UPDATE
SDE_XML_DOC2 DELETE
SDE_XML_DOC2 INSERT
SDE_XML_DOC2 SELECT