File - Export - Selected events – with Time Code please!

I am syncing the sound recorded on set from a Main recorder and a BK recorder.
The main recorder has many separated files recorded properly, with scene name and takes, while the BK recorder has a long recording of the whole day.
Once imported in my timeline and patiently resynced by hand, I created events from the BK files mirroring the Main files.
After that, I select the newly created events and do: File - Export - Selected events
Now the Main and the BK files are all the same, and the BK is a double of the main (that’s what I wanted to achieve since the beginning) but the BK loose all the metadata and despite they coud use the timeline as reference, not even Time Code is embedded.
Is it possible to fix this?