You are mixing up two things. The EOSID is the case where you have an engine failure at V1, on the ground, in a takeoff. It includes an acceleration altitude.
In a missed approach you are much higher a the start of the go-around and in many cases climbing over the runway. You can use the performance tool to check the single engine climb gradient, but there is no acceleration altitude specified. The acceleration altitude is either final go-around altitude, although some companies will allow acceleration once above MSA (and remaining in the vicinity of the airport).
If the single-engine go-around performance is limiting, some companies then specify you can always opt for the specific EOSID, but this is a little grey zone as you are mixing up two different aircraft configurations (TO vs go-around config). Ie on 737 takeoff can be flaps (1)/5/... and go-around could be flaps 15 single engine (engine failure on final).