All this stuff costs money and with the pandemic I'm assuming the musical has lost money for its investors at this stage, so I would doubt if they would go to the expense of doing it again with another band when they already recorded with MK and top session guys.
Actually the London dates at the Old Vic in 2020 were postponed and cancelled before they started to rehearse or do anything regarding the Old Vic run, and the Edinburgh run the year before was a success as they had to extend it two or three weeks more.
As far as I know the Old Vic run was suspended because after the pandemic, the person who had to direct it had several projects postponed and had to choose what to do, and also the Old Vic and many other theatres had many plays on stand by so looks like Local Hero had suffered for both reasons and was like abandoned while the rest of postponed things were being rescheduled.
Luckily Daniel Evans from Chichester wanted to revamp it and it was successful as all shows were sold out, which was easy as the Minerva Theatre is small, but now Evans is director at the Royal Shakespeare Company who has some plays and musicals in London further than Shakespeare ones, so I guess there is a chance for Local Hero to arrive to London...
But you mean the recording, not the play. Yes, it's cheaper to use the MK.demos but Evans already modified things from the Edinburgh run in Chichester and probably would modify more to London so rerecordings would be needed, by MK.and his band or the musical band... Hope it's MK!