EOSID when to follow?

[popay]

Hi there, would like to elaborate on the following issue: when do we have to follow the special EOSID on take off and go around for JAR OPS operators?
We have the RTOW charts indicating for each airdrome the airline operates, associated special EOSID. Automatically people assume that we have to follow it in case of EO, but I have been told that special EOSIDs have been published to enhance commercial load for take off performance obviously at higher take off weights, low, pressure altitudes, airfields. What is the design purpose of the special EOSID, avoiding the obstacles, laterally (deviating from original SID), on the regular SID, which can’t be avoided vertically. Another words, there is a problem with clearing the obstacles during the climb out on the departure if one engine fails. Well to start with, when do I need to follow the normal SID in case of EO?
1: if there is no climb gradient higher than standard (4,2% two & 2,5 % one engine) required and the aircraft will meet one engine standard climb out gradient.
2: if the initial turn on SID has been initiated
3: the aircraft one engine climb out performance will meet the required climb gradient, even if it’s higher than standard (e.g. light take off weight or high pressure altitude airfield).
However the book doesn’t specify when to follow special EOSID, so there are a lot of discussions whether to follow special EOSID or not. For the go around there is a table showing the max. pressure altitude can be reached single engine flaps 3. Following the logic if that pressure
Altitude is above the MSA or SE acceleration alt, than follow the published missed approach. If that PA is below MSA or SE acceleration alt, than followspecial EOSID.
I understand, it might sound a bit complicated, but that’s the way it is.
Appreciate your comments.
Cheers.