Eagle,
My take on this subject. Your scenario sounds like the first option.
1) Standard EOSID you should be able to do either. (or even at same time if you want). The 1300' accel alt is a minimum.
2) Non-Standard EOSID you must turn at stated waypoints. However you can accelerate (if you want) above the min accel alt as long as there is no V2/speed restriction.
3) Non-Standard EOSID with V2 restriction. You must turn at stated waypoints and maintain speed as directed. Can accelerate once applicable turns complete and above acceleration alt.