Just another opinion, of course, but saying that the GB couldn't believe what they were saying is like saying that we didn't believe what we were saying when we were JWs. I think most of us did believe, didn't we?
As far as voting on doctrine etc., this was just the natural outgrowth of our JW beliefs about the Holy Spirit. If anyone heard a GB pray, they didn't have any different understanding of HS than the rest of us. I'd wager that no one on the GB could have distinguished HS from gas pains or delerium tremens, although maybe FWFranz and JFRutherford made the attempts, respectively. There was no belief that HS would literally guide anyone individually, or have some special power that could be recognized when it motivated you correctly. Except for the flowery language in a few excessive assembly prayers, most prayers were about as routine and meaningless as any of those "get-it-over-with" prayers we heard before a meal or when a meeting for field service was dismissed.
Like the priest praying that God will correctly "nudge" the dice (Urim & Thummim), GB prayers for direction could not have been more than the vague idea that God's spirit will somehow "bear witness with their spirit" about the rightness or wrongness of a certain item up for discussion. In other words they might get a vague good or bad feeling or "vibe" about it. The real problem is that they thought they were supposed to abandon any personal involvement and work with a "groupthink" Theocratic arrangement, which is just another cold, bureaucratic reporting structure when you strip away the scripturo-linguistic camouflage.
The idea of a "Theocratic" arrangement was the most anti-spiritual idea that Rutherford ever had, and it makes it easy for all elders to merely go along with a system. No one has to think, all they have to do is get a feeling that something didn't make sense in the overall existing arrangement.
Getting a dozen men to vote on issues was probably just something that made sense to them, because they could rely on whether most of others also had the same feeling they probably had. Not much could change too drastically all at once, and this, of course, makes everyone comfortable that things are working smoothly, therefore correctly -- according to Jehovah's direction.
Gamaliel