I've heard good things about the Big Mind method.

Its weird to me that Zen and Buddhism would come up in the context of productivity and getting things done because Buddhism seems to say that people get stressed out because they are too attached to their work, but productivity seems to say that if you are stressed out, its because you have a problem managing your email or something, so you need a solution. Buddhism isn't about finding solutions to problems so much as it is about realizing that the problem only exists because you chose a particular ego perspective and placed a priority on it. Although doing things better, relaxation and being less stressed out may be a side-effect of a meditation practice, viewing them as the end goal can be an obstacle to realization. At least, this is my understanding.

Regarding deep breathing, I have no doubt that this activity is very relaxing, but I've from what I've read, the traditional method of practicing zen is not by taking breaths per se, but allowing breath to occur spontaneously and bringing your awareness to it, which leads ultimately to awareness by itself. Physical movement is believed to be distracting, so shallow breaths created by very small movements of the muscles below your lungs are recommended, instead of raising the chest and pushing back the shoulders to expand the ribcage and inhaling and expelling air forcefully.