Interesting. All of Orthodoxy and Oriental Orthodoxy pray for the dead and none of us believe in purgatory. Several hundred million Christians praying for the dead and yet not believing in purgatory would seem to put the lie to any notion that a belief in purgatory is the sine qua non of a belief in the efficacy of prayers for the dead.
Well, there are the aerial toll booths.
Protestants believe either that the soul is in heaven or hell immediately after death, or that it waits "sleeping" until the final judgement.
Are either of those compatible with what you believe? I am not familiar with very much about the Orthodox Church, so excuse my rather convoluted question.