Performance issue after reorganizing table in MYSQL

There is MYSQL(5.6.22-log Community Edition) database environment which has databases size varies between 1-40GB and using INNODB storage engine, it's serves for the several number of OLTP based application. We have daily schedule for "Analyze Table <>" to avoid stale statistics because of added records everyday. Besides Analyze table, I was intended to execute "Optimize Table <>" to reorganize the physical storage of table and index data for reducing space and improving I/O efficiency while access data by the application, but never successed to do in production due to time it consumes.

As an alternative, I applied "ALTER TABLE <> ENGINE=INNODB;" command to all tables as it could acheive the advantage of OPTIMIZE command. It significantly contribute to reorganize physical storage of the table and indexes in the databases as I have shown following metrics for big three tables:

            data_length             index_length                Size_MB 
            Before  After           Before  After           Before  After
BigTable1   9042919424  8312061952  8148451328  6464471040  16394.97    14092
BigTable2   2877292544  2425356288  3173138432  2286764032  5770.14 4493.83
BigTable3   1534066688  1232076800  2261762048  1955594240  3619.98 3040

I was assuming that selection on the tables will have better execution time by above maintenance.

Unfortunately, it's back fired during SELECT statements. 5Seconds report query taking more than a Minute, I have verified that before and after execution time is same and data growth is as usual. What could be the reason in this context?