One of the main questions you probably have is if it's ok - if it will fit with your beliefs - and if you'll still get all the benefits of mindfulness if you practice NonDirective - this technique which requires no concentration, and no effort.
My immediate answer is yes.
I started with mindfulness meditation, and I personally had a much more difficult time of it, and sometimes even dreaded meditating.
For me, personally, the first time I tried a nondirective technique (it was NSR) - I really enjoyed it, and it was really easy for me.
I looked forward to my meditation sessions again, but I did wonder - what about all my mindfulness? What would happen to that? What about all my compassion and the benefits I'd derived from Metta?
It ends up that it was no problem.
First off, Buddhist monks have been taught TM for quite some time now, and there are mantra based meditations, and open awareness meditations that are very similar to some of the nondirective techniques. If you even could get in "trouble" as a buddhist - it's not going to be because you favor this type of meditation over watching your breath.
The other teachings, such as compassion, the four noble truths, etc., all can still be true in your world, and in fact, might take on new meaning for you.
Personally I tack on Metta to the end of my nondirective session, and I also do a little bit of listing off things I am thankful for. After each session, twice a day.
The second reason that it was no problem, was that mindfulness in every day life became easier once I had a mediation habit that I really enjoyed - I was doing it twice a day without fail because I wanted to. And my mindfulness and compassion was off the charts as a result.
The Buddha himself would probably never want you to stress about this. Whatever gets you meditating is what matters.
As the Dahli Lama says, "My religion is Kindness."
He makes no mention of a certain type of meditation in this statement, and in most of his talks, he is encouraging humantiy to become better at whatever they are.
"Don't become a Buddhist," he urges, "Become a truly good Christian, Jew, or whatever you already are."