Could the TC Fragment be stored in the latency buffer based on the trigger time?

(This is a topic for post-v3.0.0, and it relates to long-window-readout [when the readout of the data for a trigger is split into a sequence of TriggerRecords].
The title of this Issue makes an assumption about how TC fragments are handled within the Trigger App. If that assumption turns out to be wrong, I will correct the title. The text below describes what is desired without going into details of how things might work under the covers.)

Currently, when we run with long readout windows and split the data into a sequence of TriggerRecords, the TC Fragment has meaningful contents for only one of the N TriggerRecord in the sequence of TRs. The TC fragment is empty for the other N-1 TRs in the sequence. (This has been discussed elsewhere.) And at the moment, the non-empty TC Fragment appears in the first TR of the sequence.

Could the non-empty TC Fragment instead appear in the TriggerRecord that spans the trigger time? That might better match what users expect...