If I may offer here, although not addressed to me (so please disregard) ...
This "sitting with disturbance but not in the drama" is exactly right.
We develop though this Practice the wisdom and faith to know that even our momentary "mental drama" is just drama, passing theatre, and no need to buy into it and be further pulled in beyond that. In that way, one can come to "see through the drama" even as it rages.
Shikantaza develops the equanimity of "mirror mind," having a mind like a mirror which does not judge, ruminate or reject what appears in the mirror. One allows thoughts and emotions to be as passing things appearing and disappearing in the mirror without (as they say in police dramas) "engaging the suspect." That includes strong emotions or thoughts that may come up.
For example, usually a thought of a problem comes, of your boss whom you hate, or a fear about tomorrow. Now, in Zazen, the thought of the problem or your boss appears in the mind like a scene on stage or an image in a mirror. Even the feelings of "hate" or "fear" manifest, but now they are just like scenes on a stage one is observing, or images in the calm and clear mirror. Then, one is actually the "calm" observer or "calm and clear" mirror about even feeling strong emotions and anything BUT calm and clear in that moment. One is the "calm and clear" observer even of momentarily not feeling "calm and clear." One is peaceful and equanimious about even not feeling always mentally peaceful and equanimious all the time, for it is all passing theatre. One can then see the peace and wholeness that is present and shines through even scenes of war and brokeness, much like being able to see the entire stage and theatre that is present right through any particular passing scene of war and strife in the play.
Many forms of meditation only want to feel "calm and clear." Shikantaza is a higher wisdom, being an overriding "Calm and Clear" about times of being "calm and clear" and even about times when one is not!
That is when one knows that the blue and clear sky is present, the moon is always shining, whether or not hidden by the clouds, seen or unseen. Sky is just clouds and the absence of clouds, moon is illuminating even the darkest clouds.
I hope that I did not muddle things more.