As a mechanic you will know that the listed capacity is the dry fill volume. When you drain the unit you will typically leave around 30-50ml of the 170ml dry fill volume in the unit (depending on temperature mainly) the remaining volume will sit in the various oil ways and recesses which are designed to retain oil around components such as seals and bearings during operation, in addition oil will also generally cling to the internal surfaces. As a result if you drain the unit and then subsequently force in the 'fill' volume then you will overfill. This is why the manual states to fill up to the plug rather than a prescribed volume.
Granted the amount you observed after draining does sound slightly low even when accounting for the above factors but I would not say it is as concerning as you suggest.
For reference a transmission unit of this type can easily be expected to reach temperatures of 90-120C under usual high speed running and would typically have a max design limit around 140C. Hence not being able to hold your hand on it isn't necessarily a sign of overheating.