Solid checklist. The one thing I always add: check the encoder feedback during the test run. Put the drive in monitor mode and watch the position feedback waveform for one full revolution. A healthy press shows a smooth sinusoidal curve. If you see flat spots, spikes, or noise, the encoder is going bad or has a cable issue. Encoder replacement on most servo presses is $3-8K depending on the brand, so that is a significant hidden cost on a used machine.
Also worth checking: pull up the drive fault history if the controller allows it. On Fanuc and Siemens systems you can usually access the last 50-100 faults. Look for patterns. Occasional overcurrent faults during production might just be tooling issues, but repeated encoder faults or bus voltage errors point to electrical problems that are expensive to fix.
One more thing on the gearbox: drain a small oil sample and send it to a lab. Costs about $35 and tells you more about gear condition than any visual inspection. Iron content above 100ppm means the gears are wearing fast.