you should be able to climb all the way to the maximum level of altitude limited by T take off thrust, for us 5min. we have a table for that( although EO accel is extrated from LPC which is 1500agl in most cases for us also). if you won't exceed this time you should be able to maintain your V2 to this altitude (close to 5000'agl for A320 mid weights) while maneuvering. eg. emergency turn after 1500'agl. this table is actually used to determine if the a/c will comply with the published missed app engine out. and should allow you as a captain to increase your own EO accel alt. why not climb to the MSA thrust/time limit permiting.
Lateral navigation compliyng with the EOSID of course.
let it rain please.