We all seem to be speaking the same language, with different accents?
1. No one is asking pilots to assess obstacle clearances. They should make sure that they have a flight ops perf centre that does. Find out what criteria they use. Pilots should follow their SOP procedure laid down. If you don't find it safe or correct, change it!
2. Obviously the RTOW will have the most restrictive obstacles considered stated on the chart, and if necessary the EOSID/ET will be stated - if you can't go straight ahead (distance equated to 10mins?)
3.RTOW charts have acceleration heights. The same as for the ET/EOSID, or, it may have a point (fix) if a turn is a factor (at V2 - V2+15, or whatever speed the norm dictates) that will have to be followed. ( sometimes you might have achieved your min ht for accel, but haven't got to the point for the turn on the EOSID/ET)
4. 10min eng limitations are also used, aren't they in your perf?