What to do if you're sort of a “graduate” but are past the 1 year cycle?
I feel more people have this question. In my case, I took a long vacation because I didn't know the 1 year cycle was a thing. Then interviewing became hard and it took a long time for me to find any job. Suddenly you're having a 2 years resume gap.
Is it still possible to apply for graduate positions after you're 2+ years in?
It can be hard, yes. I would look into research assistant roles at large universities. They will be forgiving of a gap year, they routinely take on people that want to use the role to get recommendation letters for MBA, MA, or PhD work. So more school will be an option for you. You can also use university research roles as stepping stones to normal industry jobs. You will be on-campus and university-affiliated so more likely to network with a recruiter who works with the university scene.