Unless you have a hook, my general feeling is that applying to a very competitive college ED won’t give you a boost unless you are in the top 25% of their students, especially if the college officially doesn’t consider interest. Your profile is pretty good, and you are competitive, but I think that for ED they are more likely to try to get as many of the students who are more likely to get competing offers from competitors.
On the other hand, are there any other colleges which you like as much as Williams? If not, it doesn’t really matter. Unless there is another colleges which you would be happy to attend, even if there was a chance that you would be accepted to Williams RD, then you should apply to Williams ED.
ED is only a good idea for a college which is on the top of your list, not for a “OK, I guess so” college. If there is a college with a higher acceptance rate which you like marginally less than William, but would be willing and comfortable attending and not looking back if you were accepted, in that case, apply to that college ED, especially if it is a college which considers level of interest. If that doesn’t work out, apply to Williams ED2.
The 3.82-3.87 GPA range is “interesting”. It is competitive for almost all colleges, including Williams, but it is in that range in which you need a compelling story. Based on your ECs, you have the ability to do so. Your GPA is within the range in which a good essay and good LoRs make all the difference.
Another VERY important thing at your GPA range is to look at your schools’ Naviance. So my kid had a similar GPA and test scores as yours, and it seemed that every school was either a reach or a safety. Based on her school’s Naviance, nobody have been rejected with even close to her stats in the previous three years from U Minnesota, Wisconsin, UIUC, Purdue, IU, etc, and even UMichigan was a match for kids with her stats from her high school. She was competitive for almost every reach in the Midwest, as well as some places in the SE and NE. But there were colleges in the NE which were no more competitive as these, which had not accepted any students from my kid’s stats (and sometimes with any stats) at all in the time range covered by Naviance.
Basically, if a college knows your high school, and there are connections, a GPA of 3.85 with a strong profile is competitive for almost all reaches, while if there isn’t that connections, a 3.85 may not me competitive for at least the high reaches (acceptance rates of below 10%), even with a strong profile.
So check out how many students with stats similar to yours were accepted to Williams recently. Also ask your GC.
What are the other colleges that you are looking at?
Good luck, you did very well, and whatever happens, you have a lot to be proud of!