Closing out games on Eve?

Hey there. I picked up Eve about a year ago in norms and decided to make her my OTP for this upcoming ranked season. I used to be emerald but now I play around gold-plat.

One of the most consistent issues I've noticed with my eve is that I tend to play "properly" for the early-mid game (chill farm, get ult, take smart picks, etc) and I end up fed with a fully stacked mejais and 0/1 or two deaths. Often times in these games, my team isn't really strong, or they're running it down, which is fine bc I understand that eve is a greedy/selfish champion and I'm sorta putting the entire game on my back by hoarding all of the gold. So what happens is I'm not really sure how to approach that part of the game where everyone is perma grouping, 25-30 min has passed, etc. As eve, how do you take advantage of your lead at this point? Do I join teamfights and just try to play them smart? Do I just sidelane? What exactly are you supposed to do to push your lead across the map once you get it? I've had plenty of games where I got ultra fed and lost anyways. Any tips?