My question involves a roommate in the State of: Nebraska

A girl and I moved in together last May. We had a verbal agreement that I would write one check for the rent and utilities and she would pay her half. Which was fine for a while. Then she couldn't work for a couple months and fell behind. She now owes me over $1,000 because the payments she can make aren't enough to fully cover. She currently has three jobs and has reassured me that she'd get caught up and current. So far? No dice.
I have written up an agreement stating the amount she owes me in back rent plus a section saying that she will pay her share of utilities and rent until the end of May (when I'm moving out because I can't afford to carry her anymore). It's on the fridge and I've made several attempts to get her to sign it. I have the saved text messages that show she knows it's there and what it's for. I put that up three days ago and she has not signed it yet.
I know it would be difficult to take her to small claims court for the rent she hasn't paid because we didn't have a written consent saying she'd pay her half. I have no documentation (other than the itemized list I have on the fridge of the fees she owes me per month) of what she owes still.
My question is - if she blatently refuses to sign the agreement, what can I do? Her name is on the lease along with mine so I can't just have her evicted can I? Or can I use the documentation I have that she knows it's there but refuses to sign it if I have to take her to small claims court?
I'm a college student so $1,000 is a lot of money - it's not something I'm just ready to give up on. Any advice?