For the sake of any other potential user searching around and finding this thread, over on this other post here it was mentioned that switching from G1 GC to CMS solved another user having a similar issue as this. We made this change on our stack and low and behold, this problem went away.
We even ran both GC's simultaneously on different nodes and the G1 nodes continued to act up while the CMS node was fine. It's been 15 days now and the CMS node hasn't needed a restart. Hope this can help any one who comes across this bizarre problem.