OP: metaphysically, there must be a classical continuation of time beneath this limit.
Indeed, not just metaphysically. Planck's constant is the smallest possible change of energy. As regards Planck length which is derived from it, from Wikipedia:
The Planck length does not have any precise physical significance, and
it is a common misconception that it is the inherent pixel size of the
universe.
Presumably that also applies to time.
In the International System of Units (SI) time is defined according to the caesium standard:
The official definition of the second was first given by the BIPM at
the 13th General Conference on Weights and Measures in 1967 as: "The
second is the duration of 9,192,631,770 periods of the radiation
corresponding to the transition between the two hyperfine levels of
the ground state of the caesium 133 atom."
This form of time is tied to local spacetime conditions, e.g. gravity, which if greater would slow down the caesium resonance, relative to a distant observer.
Newton proposed an absolute form of time: Wikipedia:
According to Newton, absolute time exists independently of any
perceiver and progresses at a consistent pace throughout the universe.
Einstein said this was unobservable, e.g. Nature, 1937, although physicists have since tried to prove its existence: Einstein, Relativity and Absolute Simultaneity, 2010. The example from Van Flandern of synchronised GPS satellites is the most simple illustration, but the concept may be inapplicable to gravitational singularities in black holes where current physics is incalculable. Indeed conventional time itself is not calculable in the plasma of the Big Bang where there are no resonating atoms. So my first reply to "could there beyond time be consciousness? What is beyond time?" The origin and nature of the Big Bang is mystery.
Heidegger's concept of time is altogether different. He is proceeding from a phenomenological basis of subjectivity, as that I of which one can be certain. His 'authentic temporality' is the time proper to the self and its constitution. Dasein is temporal, it holds past [memory], present and projected future and, inasmuch as it is one's life, exists from birth to death. Dasein has authentic time as part of its constitution. I.e. from from Kant and the Problem of Metaphysics, §34. Taft translation. (Alternate Churchill translation here.), original here: p. 189 (with my comments "*")
Time is only pure intuition to the extent that it prepares the look of
succession from out of itself ... This pure intuition activates itself
with the intuited which was formed in it, i.e., which was formed
without the aid of experience. According to its essence, time is pure
affection of itself [as in something which affects itself]*. ...
As pure self-affection, time is not an acting [external]* affection that strikes a
self which is at hand. Instead, as pure it forms the essence of
something like self-activating. However if it belongs to the essence
of the finite subject to be able to be activated as a self, then time
as pure self-activation forms the essential structure of subjectivity.
Individuals thus actualised can then go on to observe the passing of the days and eventually devise the caesium standard: as ordinary, or 'inauthentic', time. The circular argument is that Dasein must depend on ordinary time, but in the ordo cognoscendi certain experience comes first, then measurements can follow. Heidegger accepts a certain co-arising but nevertheless, authentic time and ordinary time are not considered to be the same. Being, whatever it is, as the basis of experiential existence, takes a back seat as soon as the mind starts observing thoughts and things and beings in authentic time. In my second reply to "could there beyond time be consciousness? What is beyond time?" Before authentic time and the motion of the mind there is that which enables Dasein to be, and that is loosely called by Heidegger, Being. Being is also a mystery.
Pre-conceptual apprehension, to the extent that it is possible would be a form of consciousness beyond authentic time. As Kant referred to it "intuition without thought [gedankenlose Anschauung]", e.g. Kant, Non-Conceptual Content (Dennis Schulting), p.85:
‘intuition without thought [gedankenlose Anschauung]’ would be possible, but it would ‘never [be] cognition, ’ ... ‘One
can intuit something without thinking something thereby or thereunder.
/ All cognitions come to us through thinking, i.e., through concepts;
they are not intuitions.’
