I have seen another PVR brand that can do exactly that.
If you are chase-playing live TV and press 'record', the PVR will ask you if you also want to save the current time-shift buffer.
How would this work on TVH?
TVH is generally used as backend software. The TVH API would need to be updated to save the time-shift buffer for a specific channel. A front-end (like Kodi) would also need to be updated to recognise that time-shifting is in progress and that the user should be asked if the time-shift buffer should be saved.
If possible, some EPG event data would also need to be saved along with the new 'recording'.