The airplane should be able to carry out the missed approach procedure and clear all obstacles with one engine out, if it is initiated at or above DA or MDA.
No, this is not correct. Missed Approach is based on all-engine. MDA and DA are based on all-engine missed.
2.5% is all engine...make no mistake about that. One has to remember that the Missed and EO consider the hottest day of the year for that aerodrome. Many EO procedures in AUS use 60'/nm as climb gradients.
If you call up the different procedures in the box, you will likely see completely different routes for EO procedures.(RNP)
EOSID can help you decide if you want to land at that aerodrome if you are on EO approach, or go to an alternate. Engine out procedures are not in any design criteria. You must submit them to show what would be your route, but you will never get anything but a thank you.
One reason you may see different DA's can be because of extreme cold temps. There will be a DA for temps down to -20C, then another DA for temp below -20C on baro...