Make a miniature table (with legs of less than 8cm tall) which matches the height of the plinth and sits within it and level with it, and then rest the bottom shelf on that/make it as one unit?
I realised that you can get 44mm square timber from B&Q, and that I've got some 18mm MDF. So 2(MDF)+44 = 80mm, which should work nicely as long as I've thought about how to fasten the timber to the floor.
Make a miniature table (with legs of less than 8cm tall) which matches the height of the plinth and sits within it and level with it, and then rest the bottom shelf on that/make it as one unit?