Lol, "neuralese" — that was a good one :D But you are definitely on to something as the research seems to be heading that way (too).

I watched your discussion with that Zen guy when it unfolded and I understand where he comes from -- enlightenment simply means to see through the illusion that we are not enlightened (and thus we have to become enlightened), or that we "left Eden", or that we are in bondage. Effectively, there's no such thing as enlightenment. No gain, no higher levels of anything — neither being, consciousness, nor anything else. We are already complete and perfect, whether we know it or not.

The paradox of all spiritual practices then is that one tries to become what one already is. However, saying it like this to someone who still insists that they are in bondage may lead to a situation where such a person abandons the search, does not come to the realization, ends with a notion that anything goes, and continues in their tracks. The conundrum is that one has to realize the truth themselves, otherwise it's just a theoretical understanding (or faith). At best.

You may ask, "So what?" Well, anyone who does not see their own perfection and completeness as an irrefutable fact does a lot of stupid things to make themselves so (i.e. complete), hence the existential struggle.

So to answer "what are enlightened monists supposed to do with themselves [and] what is the basis of their morality" -- and I can only talk for myself -- it's absolute selfishness. Since I know that "I" (consciousness) is and will always be the same no matter the body, mind, ideas, anything, it's in my best interest to behave in a way that minimizes pain and other kinds of suffering. And since a lot of the times I don't know what causal chain I may trigger, more often than not that means not acting at all. But that's merely a rationalization, an attempt to explain it. In reality, I simply act when I feel the urge to act. It's just that those realizations I talked about are always there to take into consideration, too. Does it mean that I act morally? I have no clue.