You did ask about LT/ST outside of the hippocampus and I did not answer your question directly but pointed you to the central nature of the entorhinal cortex / hippocampal formation (EC/HF) in the memory systems.
I feel like I left your question less than half answered.
There are several interrelated time scales in the memory system.
The shortest is actual perception.
Yes - perception is an active recall process. In the first part of perception, cells in the cortex and thalamus have some raw unrecognized perception filtering in. If this is matching some prior memorized pattern fragments, mini-columns fire in matching single cell bursts. This excites the thalamus in the tonic mode and there is a spreading of activation to surrounding parts of the map. At the same time the pattern of recurrent thalamus-cortical resonance is started.
The thalamus is interesting in that it also has connections between maps - activity in one map is passed on to prime certain surrounding maps for action. Think of this as a control signal. The reason that this is interesting is because there are matching inter-map connections between these maps from L2/3 layers; bi-directional connections that carry data. As the sensed perception is recognized this coordinated action serves to spread recognition and activation out like ripples in a pond.
BTW: The linked article on the top of this post discuss the low-level mechanism of this activation, with a focus on certain parts of the forebrain as plans are formed and elaborated. We here in the HTM community have a somewhat different view of how to interpret these findings
This recognition is never exact. In the parts of the maps where there is excitation from a strong sensation or the surrounding thalamus - but no match - the mini-column are bursting in all cells in the mini-column. This blast of signal fires the Reticular Activating Complex (RAC) and cause it to gate in more of the novel sensed pattern. (This is distinctly different than tonic mode) This is combined with the training signaling at the mini-column level causing the unrecognized pattern to be learned rapidly. I have referred to this elsewhere as the delta to your recalled memories; I like to think of this as icing being added to the recalled cake.
As you add more details in you are likely to change these memories in two ways - the pattern gains more detail about what a given pattern might be (same face from different angles or different lighting) and become more general; the other is the pattern “splits” into two distinct patterns. (different faces)
In either case - these patterns run up the hierarchy to the association areas where they form higher level object recognition and the fusion of the various senses.
At the same time other paths in the brain extract the WHAT and the WHERE of the objects and spaces being sensed. This all eventually collects in the temporal lobe as your perception of “now.”
This time scale for all this is in the range of a few alpha cycles - say 100-500 ms.
This brain-wide activation is fairly persistent and may chain from one moment to the next moment. Elsewhere I have offered how this is experienced as consciousness.
This is whole ensemble of recognition is also your short term memory. You are remembering “here and now” at long as this activity pattern is maintained. This can be from 100 ms to 3 minutes or so.
As this happens this episodic memory is experienced in the temporal lobe and through that, the hippocampus. If I understand the EC/HF correctly it memorizes faster than the cortex but only has a limited capacity - perhaps only a day or so.
As the episodic memories are laid down in the hippocampus formation the amygdala may add good/bad flavors to these memories based on the emotional perception of the outcomes of the experience.
This is a “one-day sized” buffer of collected short term sequences, with emotions embedded in the memory.
So how does this get out of the hippocampus and back to the cortex?
When you sleep your brain is “disconnected” from the body and special synchronization waves called spindles drive the hippocampus to replay the newly learned experience back at the cortex.
This spreads via the L2/3 connection and thalamus connections. I believe that the cortex is a slow learner so this experience is repeated rapidly until the cortex learns it well enough to play it back the same way it does when responding to outside experienced sensations. When the cortex and the hippocampus respond to the synchronization wave equally the training is complete.
Now this learned pattern has been transferred to long term memory and is available as patterns for perception of new experiences
More detail on the sleep/memory consolidation thing: