RH -
The way they wrote the reg once you hold a SE ATP you're locked into the post July training.
(f) Adding a multiengine class rating or airplane type rating to an airline transport pilot certificate with a single engine class rating. A person applying to add a multiengine class rating or airplane type rating to an airline transport pilot certificate with an airplane category single engine class rating must—
(1) Meet the eligibility requirements of §61.153;
(2) After July 31, 2014, pass a required knowledge test on the aeronautical knowledge areas of §61.155(c), as applicable to multiengine airplanes;
And in order to take the written after 31 July you have to complete the training program.