My 8 year old daughter has strabismus, and the muscles in her left eye continually strain to the outer corner of her eye.  To correct this, we've been doing "pencil push-ups" daily, by putting a sticker on the end of a pencil and putting it on the tip of her nose to make her cross her eyes.  Recently, I made notecards with our home address, phone number and other facts on them, and put them in plastic name tags which I clip on the front of her shirt.  This brings her eyes together in a downcast manner, thus strengthening her weak eye and helping her learn important information!  I hope this helps. 

Did the doctor recommend eye physical therapy?  That's what I did when I had this diagnosed at age 12-- it was embarassing to wear the eyepatch at that age so was more than happy to go to therapy and do eye exercises at home. They teach you the type of exercises you described and also have a bunch of machines that you look into with pencil and paper games that you do.