> reject spirituality as incompatible with science or put more effort in rational attempts to integrate them
The paradox though is that scientific knowledge is knowledge acquired through observation and reason, both of which must present themselves to an observer. Specifically, it must present itself to an observer-beyond-quality (or present themselves within a field of observation) because if we find an observer that has qualities, those qualities would be perceived by something "earlier." That is to say, if a measurement or argument is made then to whom (or in what) is it made?
Science is always limited in scope. It can only describe that which is observable (or deductions made from observation). You could extend science to include philosophy (and consider even our discussion here as philosophy) and then the limits of reason allow you only to define its own limits.
This argument has been made in some form or another by Schopenhauer, Wittgenstein, Bohr, Godel, Susan Greenfield, Roger Penrose, and hundreds of others. The One (or the Zero) is the only way to solve any problem of hard consciousness, by allowing Knowingness itself to have modulations of experience within itself.
The proper integration of science and spiritualism would seem to be that each acknowledges the domain of the other. That is, if the discussion is about the observable or rational, it's in the realm of science and made more understandable by the methods and tools of science. If the discussion is about That, quality-free substratum in which observations or deductions are made, then it is an act of autotelic contemplation. That last statement is a bit absurd. It means one can contemplate the original substratum of the Self by just being without thinking, which is exactly what the various mystic traditions have taught.
It would be a treasure if someone were to articulate this simply for a modern, secular-minded audience, in a way that would convince them to keep quiet for a few minutes and let the experience of "zero-ness" become self-evident. Even this self-evidence appears in a substratum of course, but in that moment, there's a blissful aha that would put a lot of these long essays and discussions to rest.