If you have a CE or Plus ticket you can do a Same Day Change via the app up to I think an hour before the flight you're booked on, maybe less for domestic. You don't need to call the gold line.

it seems very convoluted as the simplest solution is just to put the baggage into left luggage which is on the arrivals level of T5. It costs a bit but makes everything easier. While B2B is easy at Manchester, I believe you'll be sent landside if you want to go into the terminal. My SDC if I were to make one would be to make the Manchester trip a true B2B.