Hi RemyRabbit! Sorry for what you are going through and I know it has to be frustrating.
I definitely wouldn’t rule out the pen as an option. A baby gate that is only 2ft won’t contain a lot of bunnies. You can get pens that are a lot higher. I have seen decently priced pens that go up to 48 inches. The highest ones I have are 42 inches and they have worked perfectly.
I find pens to be a perfect way to bunny proof and a good option to contain them when needed. To be honest a lot has to due with what you are willing to put up with. For example, I have pens around my nicer living room furniture and I know a lot of people that wouldn’t want pens blocking up some of their living room like that. With that said they collapse and can be put away when you don’t need to use them.
My bunnies have their own room and are free roam in that room. I have a tall baby gate in the doorway so I don’t have to close the room up at any time. I like to think they don’t feel very secluded with this type of set up. I have come to find ways to bunny proof that works for them and the room even has wall to wall carpet.
Although your closet is bigger than a lot of people have their rabbit caged in, I have to wonder if the issues you are seeing is due to her being bored and just showing frustration. I honestly would get her out of the closet and have her in a more open area and have her in tall pens to start with when you aren’t home. I have seen height recommendations range from 30 inches to 48 inches when it comes to pens but I have yet to see anyone say 48 inches is not sufficient. Shortly after getting my buck I can confirm he jumped a little over 30 inches but he did it towards the corner of a wall and just hit the wall. He has yet to try it again but just to be safe I would definitely go for the taller pen options. That’s why I went to the 42 inch pens. The downside with those is that they tend to be a little heavy and less stable when you are trying to rearrange them or collapse them but they work.
Good luck with your girl!