There are many dedicated Timestamping Services for this Use-Case, one that has been around since '95 and with a corrrespondingly solid reputation IMHO is http://www.itconsult.co.uk/stamper/stampinf.htm. But there are other services as well, just search for "Timestamping Service"... I'd steer clear of the Bitcoin-based ones, they tend to be... enthusiastic but not too proffessional.
If you haven't yet, I suggest exploring the writings of Anton Szandor LaVey and Peter H. Gilmore (The Church of Satan, https://churchofsatan.com, https://mobile.twitter.com/ChurchOfSatan). I think you'll find very similar perspectives on the psychological power of rituals, etc.
I myself have a bit of the opposite problem: Enough is proven or patently obvious (when observing the world around me) about the psychological effects that I should believe in some, yet my brain steadfastly refuses to do so beyond verbal acknowledgement, e.g. the preceding "should". In a similar vein I've never felt awe or any similar quasi-religious emotions (e.g. when entering a cahedral, or seeing art), the closest I get is a strong giddyness when seeing how a mathematical proof will work out or a complicated story might resolve. I presume these are a consequence of my being on the autistic spectrum.