shoes are very subjective, you need to find a make/model that suits your feet and your running style. For 10Km you could probably use a minimalist 'racing flat', but if you land very heavily you might find something with more cushioning might be more comfortable.
Whereabouts are you based? Someone might be able to suggest a suitable specialist shop where you can try various different brands.
I think you might be disappointed- racing flats are generally minimalist. I've not run in the Adidas but run in flats most of the time and none of them could be described as sturdy. I'm curious as to why your feet should be sliding around though. Even using elastic laces I don't generally get foot slippage.
If you had a fancy for a 'mad as a box of fish' shoe, the Saucony Hattori seems to be available very cheaply. Very minimalist, but the zero drop takes some getting used to.
It's a little difficult to make a direct comparison as the Long Course Weekend uses a different (and much hillier) run route to the actual IM course. I did the bike and run back in 2012 (missed the swim due to me forgetting just how far away Tenby is). I was able to run harder/faster on the Sunday than when I did IMW in 2011, but the end result in both cases was in the same ballpark (ouchie wise).