So, it's been a hectic couple of weeks and I've only just got around to looking into this with any great detail. Thanks to everyone who put suggestions forward, as always I really appreciate the help!
First off the fixes; what I've ended up doing is removing most/all of my code from the VBI and only use it to set a flag which I then check for in my main loop to trigger the screen update (tip was found here:
https://eab.abime.net/showpost.php?p...9&postcount=69).
Second fix was the issues paraj mentioned above; restoring the OS screen in the correct place when exiting, and owning/disowning the blitter when jumping between the system and back to the game.
That all works great.
Regarding the missing graphics when jumping to the system, of course ross and paraj were spot on with their analysis and when I think about it, it makes total sense. Adding the hack did solve the issue, but the final fix I applied was just enabling the bitplane DMA pretty much straight away, before I store the system DMA in any case, so switching between the game and the system always leaves it enabled.
Problem solved, and once again, many thanks to the people who made suggestions and fixes. On we plod...