Assuming your downpipe is already removed, Transfer case is 5 17mm bolts, remove those and wiggle it off the output shaft (may need to lightly pry in multiple spots to get it to begin to slide on splines). once off the trans, you can slide the transfer case off the driveshaft or just support it on a block under the car. remove all appropriate electrical connections etc. disconnect axles and it will be ready to support and remove the 4 motor mounts.

Alright; at what point during this should I remove the cross member?

You don’t need to remove the crossmember just the piece that goes to the radiator support and front motor mount

There are a few plugs left to remove and u will need to either remove starter or just disconnect it from harness, front and side motor mount, side and rear trans mount, unbolt the 2 bolts to carrier bearing, disconnect water lines and U should be good to pull it out. I pulled mine with the harmonic balancer on as it was froze just takes a little more manuevering.