Well I managed to get hold of a spare wheel, so out came the insert for the accessories, and in went the spare:

. . . then I put in my bits & pieces:

I found some 3mm PVC sheet, which isn't quite rigid enough - I'd have preferred ply or similar - but if at some point I decide to re-visit the project, I've now got the template. I joined the bulkhead section with some small hinges I had in the Man Drawer in the kitchen:

Then I acquired some thick heavy duty cloth to cover the board, dark grey was the best match I could find, and stuck it on with hot melt glue:

Job done!

As you can see it's far from perfect, but better than a wobbly boot insert with recess. OK - you lose some space with the recess gone, but time will tell if that proves to be an issue.
To finish, I'm gonna try to get some of that spongy sound-absorbing material to stick underneath the board which will also act as a cushion, and as Malroy mentioned, try to fabricate some sort of circular insert for the spare wheel itself for the wheel brace and nuts etc.