I had to make a throwaway account just to respond to this post, because I empathize with you and am in a similar predicament. The first thing I want to say is that you shouldn't have been written up. It's not your fault you have nothing to do. It's your management's fault for not understanding your position or lack of workload and not making any efforts to develop you as an employee. You are a valuable asset, ready and willing to work and they aren't taking advantage of that. That's their problem.

My job is excruciatingly slow. I have gotten to the point where I feel like my skills are wasting away and I'm basically invisible. If I get an email or a task, I am so grateful to have something to do that I get excited and finish it right away. Then I'm left with...nothing to do again. I have tried slowing my pace but that just seems idiotic (like "I'll sign this half of the paperwork and then in another thirty minutes I'll sign the other half"). I have tried requesting more work (which is a slippery slope because it indicates that your position may not be crucial or could be cut down or completely sacked). I decided to take that risk. I was told that I was overestimating how much extra time I had when I offered to take another department's excess work so they wouldn't have to hire a part-time person. I was told I could look into taking a Microsoft course or something. That would keep me busy for maybe a few days and then I'd be back in this mental prison. There have been numerous times when management gets really pumped up and starts exclaiming about how busy it's going to get. I had one of those days last week. "Super slammed" for me means 3 hours of steady work in a day instead of about 1 hour.

I am afraid of looking like a job hopper but mentally I can't take it anymore so I have started to apply for other jobs. People who have never experienced this brain-sucking boredom will think I am having a "first world problem" and that I should be happy to have so much time on my hands. Well, I come to work to actually work, not to read the news or Reddit until my eyeballs fall out. Having too much work is rough but I have discovered that having too little to do is awful in an entirely different way. You start to devalue yourself, question your worth, and fear for your future. I wouldn't be surprised if my position was cut or reduced but I am hoping to get out of there before that happens.

Best of luck to you. I hope you find a company that wants to invest in your development and entrust you with responsibilities.