The thing is that although training in parallel double octaves certainly comes from the piano background, we have to remember the origins of the modern legato school of playing the organ. That would be piano.
Often organists who didn't have systematic training on the piano before they take up organ studies, when they see pieces like Prelude and Fugue on BACH by Franz Liszt or chorale fantasias by Max Reger (among many other works composed after 1850s), they recoil in fear - these octaves seem pretty scary.
Today's sight-reading piece is an excellent example of this technique. This is the March, Op. 7, No. 1 (p. 1) by Augustin Barié (1883-1915), a blind French composer and organist. Barié was a student of Vierne and Guilmant who sadly died at the young age of 31 of a brain hemorrhage.
Even if you are not a virtuoso on the organ or piano, I encourage you not to fear this piece (or any other piece for that matter). So often we shun ourselves from great works because we think we are not ready to play them.
Yes, we may not be ready to perform them yet. But there's a huge benefit in sight-reading difficult music, too. Of course, you have to be conscious that the result will be extremely slow tempo and thinner texture, perhaps separate parts. Remember that we don't change the exercise, we change the scaling.
One more thing: have you noticed that the best modern organ method books feature special exercises taken from the real organ compositions? Incidentally, pedal part will serve for this purpose, too because of double octaves and passages in the high range of the pedalboard.