Your PRD DB Size of 2,3 TB is relatively small, and you definitely have enough HW resources to start TDMS Roll-out project.
Your goad should be to achieve STABLE run first, than you can gradually improve performance using different technique, described in "How-to Improve Performance for Data Transfer" Guide.
Troubleshoot proactively,check all logs, ST22 dumps etc. In the actively running Production environment your worst 'enemy' could be annoying ORA-1555 (Snapshot too old) error - so fine tune DB indexes and collect fresh Optimizer statistics to avoid inefficient long-running SELECTs on the largest frequently changing ERP app.tables. Preferably run TDMS package when PRD system is at rest.
Good Luck,
Andrei