I have enlarged a cockpit on a S&G kayak. A plywood stacked coaming can be removed quite easily with a chisel. Just split the first shim up from the deck parallel with the deck, then shave off the remnants carefully with a sharp chisel then finish the last of the removal with ROS sanding. There should be glass and epoxy between the deck and the shim stack so sanding into the fill coats is a no brainer. If your new coaming is larger in all directions it is easy to enlarge the deck opening to match. If the new coaming overhangs the deck opening a little that is no big deal and will not show unless you do headstands in your cockpit.

I would suggest you should be happy with your seat location, i.e. the trim of your kayak for weathercocking, because this is also the right time to move your seat and coaming back to eliminate any weathercocking. If the rear bulkhead gets in the way you may also consider moving it back.