I think this problem of “robotic Judaisim”, as the OP so eloquently put it, affects the vast majority of Jews alive today. IMHO, it is the root cause of almost every issue we face today (OTD kids, abuse, chinuch, etc).
It is absolutely crucial that we learn feel Yiddishkeit, not just “do” it. We have to make sure not to get so bogged down that we are just going through the motions, without it meaning a thing to us.
Practically speaking, I think the most effective ways of getting this connection to Yiddishkeit and Hashem back are:
1) Going through davening, both its translation and its in-depth explanations. Our Davening is supposed to the basis of our relationship with Hashem, and going through davening can show you what that relationship is supposed to look like.
2) Learn Mussar. The entire point of Mussar is to make Yiras Shomayim and Ahavas Hashem “real”. Once you acquire true Yiras Hashem (realizing how truly great Hashem is) and Ahavas Hashem (realizing how much Hashem id constantly doing for you, because He loves you), doing Mitzvos will naturally become an outpouring of that