Just use one forklift/loader and one lifting strap right in the center of the auger. Then you can tilt it as you lift out.
Pretty sure right side comes out first, as left side is auger drive and that shaft is fixed in place.I have removed a few augers on new 600 series R and F headers. If you move the reel all the way up and forward you can then move the auger out of the top if you have two forklifts or lifting sources. If you dont have to change the insides of the auger you can take it out and back in in about a day. You can push the shaft on the left hand side in flush in the auger and leave the right hand side where it is. Start lifting the left side first then pick it out. Hope this helps.