The ball is definitely in the Archdiocese's court, as it depends on whether they take this decision to the High Court. Personally, I am sure they will, and this will mean more delays for everybody.
I haven't posted any quotes, as I'm not a lawyer, and don't want to muddy the waters. By my understanding, though, the Archdiocese needs to submit a brand new planning application, as their current one has been rejected by the inspector. That means proper public consultation on new plans, and a full planning committee to consider it. If they have used their appeal time well, that could happen quickly, but if they have not worked on a plan B, then it could take time.
I'm unclear about the legal reasons for the ammendments to the notice, but wonder whether it means drawing a line under the mess, and start afresh with a new application. That way, the nightmare confusion of paperwork in this one doesn't slow the process down. As I said, though, that's just my uneducated guess.