After looking through help files and forums, I finally came out with the solution to my problem (with the help of many online contributors of course). The solution, as expected, has to do with the rest ring that eagle sets.
Initially the rest ring was set at a min value of 10 mil for my DRC file. I lowered the value of that to 6 mil to avoid overlap on the header.
NOTE ON THIS: BE CAREFUL WHEN SETTING MIN HERE BECAUSE EAGLE SETS THE MIN FOR THE WHOLE BOARD, SO OTHER COMPONENTS WILL ALSO BE AFFECTED. FOR MY CASE, EVERYTHING CHECKED OUT GOOD, BUT TAKE CARE IF YOU USE THIS SOLUTION.
I think it would be more convenient if you could individually set the rest ring size for specific components since you have components of different sizes on the board, however, I don't know if eagle has such capability. Please correct me if I am wrong.
Anyways, hope this helps someone else out there. I spent quite a bit of time trying to find a better solution than just modifying the rest ring size for the board, however, I wasn't able to find anything else.
Also, for those who didn't read the comments on this question, here is another resource for anyone who has stumbled here with a problem with Via diameters: VIA DIAMETER PROBLEM
To add to the solutions. I re-posted this question one element14 community forums for Eagle. Here is the response I got.
There's no reason to go with through hole. There, I said it.
With a decent microscope, a pair of soldering irons (to lift double sided components), hot air, solder paste and some flux you can easily solder components and modify things. I do 0201 on a daily basis with this setup. 0402, 0603 are no big deal. Also TSSOP, QFNs can be soldered (QFN with flux and hot air is pretty easy).
Through hole forces a completely different architecture for the board layout and the results of using a through hole design could differ, especially as it concerns EMI (think FCC certification). You want your board to resemble as close as possible the final product. Through hole requires space on both sides of the board for the holes and so wastes precious PCB area. Smaller PCB usually means lower emissions too (as well as lower costs etc).
BTW, this doesn't mean the whole design has to be surface mount. 32kHz crystals do come in SMD. There are plenty of them at digikey.
I realize this is an opinion but the reality is SMD isn't the terrible thing that its been made out to be, even for hobbyists.
Best Answer
Asked before: What exact header is this? (and others)
So as mentioned in the linked post it is these:
https://www.digikey.com/en/products/detail/digi/76002056/3481914?s=N4IgTCBcDaIOwDYAMSxIKwJAXQL5A
It appears to be obsolete though. I get some strange hits via octopart on the partnumber 76002056. It directs to the devboard and not the socket. (sortof; is that price correct?)
It seems to me that these are something properitary to digi. I would reach out directly to them. I have no idea, but they might sell them directly to you. Worth a try anyway.