I think you should probably set up sde (wherever),
then setup another sde in postgresql using the postgis data type pg_geometry.
Then utilize the gdb tools to create a replication database.
Here is some esri help
NOTE: This will require duplicate licenses if both dbs are not on the same machine and both in postgresql

Consider setting up database replication on the original 9.3 db.
It doesn't work as well as the new 10 does but...
replicate that to another sde in postgresql using the postgis data type pg_geometry. 

Here is some esri help
NOTE: This will require duplicate licenses if both dbs are not on the same machine