I'm not sure whether something more specific will be ever published. The whole LAPL thing relies on national authorities (such as CAA) for a number of things. The application forms, whether GPs will be allowed to issue LAPL medicals etc.
In my view, the LAPL wording is so loosely designed to allow maximum flexibility for each member state. More importantly, it has to be so vague to make sure that it doesn't interfere with the NPPL as it stands in the UK. Don't forget that the LAPL is basically an extension of the NPPL.
My interpretation is that we (in the UK) will be able to get the LAPL medical using the current DVLA guidelines. But that's my speculation..