We proclaim in our liturgies "The holies are for the holy!" as a warning and reminder to all the gravity of taking communion unworthily, and the high standard to which we are held as Christians. That is incompatible with any kind of laissez faire attitude towards communion, but obviously others have a different standard. This may be one of those things that the Episcopalians allow (I have no idea; I've never been to an Episcopalian service), but even that would not solve the personal turmoil within the person who may not believe in the Christian faith -- that Christ, Who definitely existed (not even anti-Christian scholars like Bart Erhman doubt this), was incarnate, lived, preached, and taught, and at the appointed time gave Himself up willingly on the holy wood of the cross for the salvation of all who believe in Him -- and is thus struggling with the idea of taking communion.
That is why I counseled earlier in the thread that you should figure out what you believe before tackling what you should (or shouldn't) then do. It is not only about what is allowed in a particular context. Holy scripture teaches us that while all things are allowed, not all things edify. The reception of the Holy Body and Blood of our Lord and Savior Jesus Christ is certainly one of those things that should edify (and really much more than that; in Orthodox theology, it sanctifies and deifies man, but that's another topic), but as neither Christ nor any church that I am aware of can force Christian belief upon anyone who shows up to their services, it is best to rely again on scriptures that caution against receiving unworthily in those cases where there may be some grey area.
And really this is not one of those cases anyway. I will state it plainly, with the utmost respect for what I perceive to be a real dilemma in the mind of the OP and the context of a church that would allow him to receive even if he does not believe: In the normative practice of all Christianity (i.e., Orthodox, Catholic, Protestant, Nestorian -- literally all of them) throughout time, a person who would partake of the Eucharistic sacrifice without believing would by definition be receiving unworthily. Lacking true Christian belief makes the recipient unworthy to receive, and hence they would condemn themselves according to the standard of the scriptures, regardless of how nice any particular church feels like being in letting non-believers receive.
I do not phrase things this way to condemn anyone or any church, but to remind as to the biblical and historical standard, still kept to by many churches (including my own but of course also many others). This stuff is not to be taken lightly. Condemnation is very serious. I would not want to have to answer for such an act, and have in my own past therefore voluntarily removed myself from communion (and here I'm talking for three years before becoming Orthodox) with the Roman Catholic Church which I was then a part of, out of respect for the seriousness of what receiving communion there means. There really isn't any space in any form of traditional Christianity for doing anything else, because traditionally communion is also a sign of visible assent to theological and ecclesiological unity with whoever you take it from. This is is why I couldn't now receive from the hand of an RC priest, even though they allow OO and EO to receive from them; it would mean automatic excommunication for having sought a sacrament outside of the Orthodox Church. I'm sure you know the strict ecclesiological standard held to by the EO since you were once one, OP, but then imagine if your standard was even more restrictive by virtue of having only accepted three councils, as is the case with the OO. I cannot receive from hardly anyone (okay, there are ~ 90 million of us, but only in six churches, compared to 20+ for both kinds of Chalcedonians), and yet I press on because I believe this is the correct place to be. Do you believe the same about the Episcopalians? It doesn't seem so, if they are traditional Trinitarian, Christ-believing Christians (which I thought they were; someone please correct me if that is wrong) and you are not sure that Jesus Christ even existed. Those two things can't be in unity with each other, so why would you act as though they are by taking communion there?
I hope this doesn't come off as haranguing or speaking negatively of others, as that is not my intent. I just hope that you will really think about what you do or don't do and why, because communion is so important on many levels beyond "Will they allow me to or not".