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When the bridge bulge looks like this I assume the bridge plate is split.

What is the process to flatten the top before gluing in a new bridge plate?

Or is the top too far gone and needs to be replaced?

this happens when braces loosen, or bridge plate splits
EASY FIX . Check for loose braces also. Remove bridge.
https://www.youtube.com/watch?v=TYg8sEjxgpc
A remove bridge plate, I use a wet sponge , it may take 24 to 36 hr. Get a cello sponge and cut to the shape of the plate. Make wet. You want it wet enough to hole water without it slopping all over the place. Rewet a few times through the day.
https://www.youtube.com/watch?v=1Hp8yfVI-J8
I use a spreader knife from Pampered checf but an artists pallet knive will do the trick. Don't force it, take your time and after about 6 hr of soak see if you can work it in under the plate. If you can keep it there as it soaks.

Once loosen you want to work across the grain of the top. . Also note the loose braces, and when the plate comes out and just clean out the old glue. Get a plastic caul and clamp flat . let set for 2 days and then take out the caul and allow another day to dry, Sand off the old glue , reglue the bracing, then make a new plate and glue in.
all should be back to normal,

Thanks John!