Bare awareness while meditating in the Mahasi Sayadaw tradition

As far as I understand, noting only ceases upon cessation(nibbana) itself.

That is to say, the meditator does not stop noting.

I'd also invite you to meditation.sirimangalo.org

Ven. Yuttadhammo gives Dhammapada talks there on Tuesday nights, 9pm eastern time, Dhamma talks on Thursday, and does Q & A Saturday nights.

He also offers 1 on 1 meetings in an online meditation course format for more serious meditators, so this may be of interest to you.

As mr. Ryan sad, "As far as I understand, noting only ceases upon cessation itself." (Sadhu!)

Mr/Mrs PaPa, not much in certain styles in this matter, but one should gain minimum/any of the Jhanas, so that it would make sense to let go

...And here is how I understand the Dhamma taught by the Blessed One: 'When the monk is percipient of himself here, then from there to there, step by step, he touches the peak of perception. As he remains at the peak of perception, the thought occurs to him, "Thinking is bad for me. Not thinking is better for me. If I were to think and will, this perception of mine would cease, and a grosser perception would appear. What if I were neither to think nor to will?" So he neither thinks nor wills, and as he is neither thinking nor willing, that perception ceases and another, grosser perception does not appear. He touches cessation. This, Potthapada, is how there is the alert step-by step attainment of the ultimate cessation of perception.'"

"That's right, Potthapada."

"But, lord, does the Blessed One describe one peak of perception or many peaks of perception?"...(see further DN 9)

Just to see (and understand) that it (how it works everywhere at least) is actually not a different phenomena in the "Mahasi Sayadaw" method and also not in others which are in line with the Dhamma, in what way ever one accesses certain samma concentration:

...But as the latter is able to suppress the hindrances just as access concentration does,[23] and since it is the neighbourhood of the noble-path attainment concentration,[24] therefore that same momentary concentration is spoken of by the name of "access" (or "neighbourhood") and also the meditation subjects that produce that momentary concentration are called "meditation subjects leading to access concentration." Hence it should be understood that momentary concentration, having the capacity to suppress the hindrances, has also the right to the name "access" and "purification of mind." Otherwise purification of mind could not come about in one who has made bare insight his vehicle by employing only insight, without having produced either access concentration or fully absorbed concentration.

Its merely just a "dispute on the emperors beard" (as a Austrian proverb expresses)

As AN 9.36 points out, one can attain cessation based on any of the levels of jhana. Thus, although the specific level from which cessation is attained might differ from person to person, its role in functioning as the basis for cessation is the same in every person's Awakening. (Note to DN9)

(Note: this answer has not been given with the agreement to be means of trade or the purpose of/for trade and/or keep people trapped and bound. How you handle it lies in your sphere, but does not excuse the deed here either.)

The noting shouldn't stop one from seeing things with bare awareness. One doesn't focus on the noting, one focuses on the meditation object.

...at what point does one dispense with the conscious labeling...

If one isn't consciously aware of the noting then one will be unconsciously (un)aware of the noting. We note no matter what we do.

When we need to listen, speak, read, write or study then it is more difficult to note consciously. Some don't note consciously in these situations but they do continue mindfulness of bare experience.

I've never heard of an end to noting(conscious or otherwise) made by conscious effort or made by a non-volitional event.