Well now my wind down is much shorter 'cause he can go to sleep by himself, but i remmember it used was pretty long, i used to take him to his room, sit on the chair and read a small book in really soft voice, then i would swaddle him, put him in the crib, close a bit the curtains (not all the way, just a bit), give him his paci, and then if he started crying i would start the pat-shush. But i guess singing two songs is pretty much the same as reading a small book, so... i don't think that is the problem.
I guess in your case what i would do, is at the 1hr 15min he has been awake, then i would start the wind down, this will only buy you a few more minutes 'cause of course you don't want him overtired, but little by little he will be abble to extend his awake time. And if he is awake that amount of time, he is acctually "napping" for 2hrs 15 min, rigth? my DS used to need larger naps than recommended too.