You may find tearing up that 3/8" layer to be more work than laying it in the rest of the house. Cutting it out around the cabinets may also be more difficult than removing the cabinets and re-installing them. I can generally remove cabinets for re-use in about 1 hour (average size kitchen) assuming no granite counter top.
A little more support on the rest of the floor wont hurt anything but make sure you lay any new plywood in the opposite direction of the existing sub-floor. I usually glue it down to prevent squeaking issues. I think you may find this faster than demo on the existing stuff especially if that is glued down also (may or may not be). One last thing put sound deadening underlayment (it comes in rolls) down this greatly reduces the echo effect a lot of people don't like about wood floors.
A little more support on the rest of the floor wont hurt anything but make sure you lay any new plywood in the opposite direction of the existing sub-floor. I usually glue it down to prevent squeaking issues. I think you may find this faster than demo on the existing stuff especially if that is glued down also (may or may not be). One last thing put sound deadening underlayment (it comes in rolls) down this greatly reduces the echo effect a lot of people don't like about wood floors.
