Replying to my own issue, found a fix on the Plex forums (thanks to Macieksoft).
I had the following setting populated on my Plex server:
Plex>Settings>Network>List of IP addresses and networks that are allowed without auth
Deleting my local IP address / subnet mask entry from here (leaving it blank), fixed the 40+ sec launch time for any media playback I was experiencing.
This affected Plex .033 on the OSMC and LibreElec Kodi 19.x releases, Kodi 18.x not affected.