I would suggest first calling BA and seeing how much it would cost to change the existing booking,

Looking on EF, would seem that the change fee would likely be GBP300 plus GBP28.5 additional surcharge. Probably more expensive tan a one way economy ticket, but have all the protections of a through booking, can check bagage through and just take a flight around 17:30 from MAN to connect. No need to worry about missed connections