I have been at the Resort for NYE three times in the past four years. It is my preference to be in DCA in the afternoon and evening because it is much less crowded than DL. Our normal routine is DL at rope drop and have a reservation at a table service place for breakfast (such as Carnation). We do this because the lines for food start getting really long as the day goes on.
We hop over to DCA in the afternoon to avoid the craziness of DL, people start camping out in the Hub in the morning. It gets difficult to navigate DL around noon or so. As we were leaving DL around noon we passed the line for lockers, which was backing up Main Street!
We have never had a problem entering/exiting DCA throughout the day. Not to say this couldn't happen this year, but historically it hasn't been an issue for DCA. We actually went to the Hearthstone Lounge last year around 10pm for drinks and went back into DCA around 11pm or so with no issues. We used the GCH entrance. There were absolutely no lines.
We have gotten FPs for the midnight WOC in previous years. Be prepared to get there early for a good spot. Nowadays we don't even bother with WOC FPs because only the "pre show" is different. There is normally a lead up to the countdown and then a "fireworks and fountain" show. There are no projections or anything, so we just watch from the area by California Screamin'. The fireworks are above us, we can see the colored fountains, and we can see the DL fireworks in the distance. It is uncrowded and after the fireworks we hop on TSMM with no wait.
But this is just our little secret, ok?
My tips:
-avoid DL in the afternoon and evening if you can. If you can't, be prepared to hang out all day.
-make reservations for meals because the counter services lines are LONG
-bring your patience, moving through the Resort will take longer, just expect it and roll with it
-ask before you exit the park if there are any restrictions on re-entering at that time, obviously things can change quickly, but it saves you from exiting if restrictions are in place
-unless you are dying to watch the same WOC show that you can see tomorrow, there is no real reason to be in the WOC area. If you really want to do WOC, get there early and be prepared to wait.
-an alternate experience is at the Mad T Party in DCA, they do a countdown iirc and this spot has live music and a bar. Great spot to hang out.
-bring cold weather gear, lots of people ended up buying sweatshirts or blankets because it gets very cold, especially if you are just standing in one spot.
-order your adult beverages way ahead of midnight if you want a glass for toasting, the lines are LONG
-since you are staying at the GCH, this doesn't apply to you, but for others who might wonder, it is best to hang tight after the midnight fireworks and not hurry to the tram/bus. The entire Resort will be headed that way. Just wait for the parks to empty a bit before attempting to leave. Or stay within walking distance if at all possible, it is totally worth it!
-New Year's Day in the morning is soooo uncrowded for the first couple of hours, so if you can swing it, try to be at the gates bright and early.
Have fun! It is a great way to ring in the New Year, we love being there for it. Yes, it is crowded, but it is doable if you just know where to go. I would never personally do DL as it gets really uncomfortable, I mean shoulder to shoulder in some spots. DCA was never that bad.
The Fireworks and Fountain show can be viewed from the Screamin' side as it is all fountain based (no projections). But I wouldn't recommend watching the actual WOC show from Screamin' as you just see the backside of the projections. 
