No reason to remove that section other than to access framing to install the new ceiling joists(if necessary).

CnC's advice about venting is very good. Am not sure why access to the space is necessary.

You could leave the drywall, but you should have access to the newly created attic over the kitchen, so at least a hatch or opening in the wall would be necessary.

Also don't forget about ventilation of your new attic space! In that regard, opening more of the drywall would help, especially up high, (assuming adjacent existing attic is properly vented). Otherwise you'll need to add venting to outside.

Thanks for the tips! I do intend to add a small scurry hole so I can blow in insulation to bury my IC-rated canned lights.