Slipping the SIM card in first is a helpful suggestion.
My motherboard actually was not quite lined-up as mentioned, and so after the SIM didn't fit, I was able to pull and reposition the motherboard properly before proceeding.
Quote from johnhart:
Although I would say "needs to be slipped under the clips on the side". The most obvious clip is next to the camera, facing south (if the camera is in the NE corner). There is a corresponding clip on the opposite side of the north end the logic board, facing east (a bit east of the #6 ribbon cable).
It's still possible to get all the screws back in with the logic board above the clips (trust me), but it's a serious barnus because the SIM card holder won't fit back in and the camera will be pointing a bit askew ... and you'll have to pull all the screws back out and figure out what you did wrong (and why you had a naggling suspicion the logic board wasn't placed quite right).
I would recommend sliding in the SIM card tray *before* putting any screws back, just to make sure.
If you've made it this far, you've probably realized that you underestimated the work involved. You can finish, but it's going to be painful.