I guess I'll take a stab at this then. We have been to the parks for NYE a couple times. To be honest, we leave DL by 10:30 AM and don't return because DCA is far less crowded and more pleasant to us. Unless crowd patterns change significantly from previous years, you are likely to be able to get in to DCA any time that day/night, but DL could experience gate closures.
If the weather is good, there will very likely be gate closures at DL, so the rule of thumb is to be in DL by early afternoon if you want to be sure you are inside. I have seen others suggest 1 PM, but there's really no way of knowing when crowds will peak. The thing about gate closures is they are unpredictable. They may happen, they may not. They may happen early afternoon then lift for a while in the late afternoon or evening then close again then lift again or they may just hit a closure and mostly stay closed through all the interesting parts that you wanted to be there for. You just don't know for sure, but NYE is one of the most likely days of the year when gate closure will happen.
We had friends who chose to stay on the DL side 2 years ago and they reported wall-to-wall people and lines for everything that eventually just got too long for them to tolerate. Fastpasses disappeared fairly quickly that day, but I don't know how quickly. Ordinarily I would expect headliners to be gone by 3 PM on NYE and think there could still be some HM left, but then again HM is a very popular ride during the season. Also, MaxPass has really changed fastpass availability patterns.
I can tell you that DL will not just let you in with a dinner reservation if the gates are closed. I have heard that these closures are hard closures mandated by the fire marshall.
