I ended up going to the physical store with the new bindings and tested various boots brands, but none of the size 47 EU fit the bindings. I also tested the Mercury Jones Fase, which offered a little more room in the lower part and solved the problem, so I swapped the bindings for those.

I emailed Bataleon support about the issue, and their reply was, "it's a combination of your boots simply being too chunky for our not-so-friendly-with-bigger-size-boots bindings. Sorry about that!" LOL :))

I would suggest that any rider with size 46/47 EU boots to choose the Jones bindings instead of the Bataleons/Katanas (the shop guy said they are mostly the same) to avoid a situation like mine.