Guys and gals thanks for the great feedback and debate.
Pool, it's a fair point and one we've discussed in training the procedure. If you get a turn at min alt from tower it will be because the ATCO feels it critical. Part of our checklist in the tower is for the two runway controllers to talk to each other and establish the best separation plan for the traffic scenario before giving any turns. When we've done this in our sim the missed approach is invariably at or above 1000'.
Your workload issues at the early stage of a go around are known to ATC.