It seems to be part of a "successful" BK to believe and not believe at the same time. The believing part being about fitting in socially, being accepted and achieving status. The not believing part being about carrying on as usual, in opposition to the beliefs, eg amassing wealth and building properties that, logically, would be pointless if the world was really going to end in 2 to 3 years time.
Well, my opinion is little different. I feel (may be wrong though) that to be part of a "successful" BK either you have to surrender your intellect 100%, or use your intellect 100%. We get into inner conflict when we mix these two.
The believing part being about fitting in socially, being accepted and achieving status
My advice to anyone who is already in BK or planning to join BK is that never chase any of these ('getting acceptance'/status within BK etc) or your spiritual growth will stop. Being on 'receiving' side of acceptance is OK for initial few months (max 1-2 years) to heal oneself (If healing is required) but once healing is complete better try to shift to 'giver' side as soon as possible (to even those from whom your were receiving acceptance) and stick to your inner consciousness. If you will chase 'giving acceptance' to all, you will always feel that you are progressing on your spiritual journey.
I failed as a BK because I was too logical, valued integrity too much
Well, I understand what you are saying.
But when I deeply checked these two concepts, I realized that being logical and valuing integrity are little subtle then these appear at surface.
We often miss the variable 'outlook' when we validate 'logic'. Two people having same logical mind may take different decisions if they have different outlook of the situation.
Similarly there are some hidden variables (role, outlook) to validate integrity apart from visible parameter like values. In general telling lie for a person whose value is 'speaking truth' should be considered as violation of integrity. But if enemy country catches him and asks for some secret details, then telling truth will be a violation of integrity.
So if we feel that someone is telling lie, it either means that he is violating integrity or we don't understand his outlook. May be his role demands it.
[Will be busy for next 1-2 weeks. Please expect delays in reply]