Bags usually takes less than 30 minutes for domestic GA, but if the plane lands on terminal 1, taxiing to terminal 3 could take another 30 minutes on a busy afternoon or morning. To get to terminal 2 from terminal 3 will take less than 5 minutes on the shuttle train and it runs every 15 minutes or so. CX would usually still allow check ins up to 30 minutes before scheduled departure time even with baggage, so your 2,5 hour layover is doable.