FFS Vlad, why are you finding this so hard? It isn't rocket science. If you want to convince people that your god is more than just a guess and that any other guess is just as good (leprechauns), and you don't think the methods of science and logic are up to the job, then it's up to you to provide such a method and tell us why you think it's valid and applicable.
Other people are under no obligation to help you, this is a hole you've dug yourself into.
I think whether people find a particular interpretation of an abstract proposition convincing would depend on the individual. Abstract concepts such as goodness or justice or gods cannot be objectively detected or demonstrated and BHS and I will have to agree to disagree that these concepts have more coherence than concepts of gods. So far I find BHS's arguments unconvincing. Maybe if we could define justice, fairness, equality in any kind of objective way or even agreed upon way rather than trying to define them using more abstract concepts, or if we could detect their presence using science, or if those concepts were made up of matter that can be measured, I would find BHS's argument on there being a difference in coherence between gods and goodness convincing, but as that is not the case I don't see the difference between those concepts and gods.
That is not to say that BHS can't find gods more incoherent than goodness but I don't see that as something that can be demonstrated as objective fact. Yes I understand that with gods some people are theorising some kind of duality with an alternative space and time (or no time) that is undetectable, but to me that duality/ alternative dimension/ universe - whatever you want to call it - is just another abstract concept.
Obviously in order to understand a particular concept the brain has to comprehend the words and reason and interpret them with reference to knowledge of the material world. But science is somewhat irrelevant in this area, as Gordon said. I think where scenarios are offered that transcend science and the material world, that is part of the attractions for some people because the idea that you are not limited by science but are in the world of abstract concepts such as good and bad, thoughts and intentions, justice and purpose and a spiritual accountability (if you believe in a concept of souls) where worth is measured by good and bad deeds and intentions rather than your material body or assets can be appealing.
Deciding between abstract concepts such as right and wrong (as opposed to legal and illegal) could also be described as based on a guess or choices could be justified by argumentum ad populam or argumentum ad consequentiam. Decisions are based on feelings and the reasoning out of potential consequences, which from my experience is similar to decisions about religious affiliations. In which case I do a lot of guessing in my life and see no reason why guessing about gods is any more problematic for me than all the other guesses I make. I encourage my children to guess and adopt faith positions because it is normal behaviour for loving parents to pass on as advice any guesses, behaviour and thoughts and abstract concepts they feel have been beneficial to them.
I would say that where theist guesses are convincing to others whereby they join a particular faith, it would be based on the others feeling something (curiosity/ affinity/ fear) when reading a particular religious text, or feeling something when in a particular religious building or listening to a particular sermon or in discussions with groups of theists or participating in specific group or solo rituals such as prayer. If "guess" covers that then fair enough. It therefore makes sense for theists to keep offering others opportunities to try guessing for themselves and see if their response and interpretation to the experience has beneficial consequences for them - regardless of whether the response is theism or atheism.