So when you say her mates are passing her up, do you mean they weigh more? I would feel her breast bone and crop to see how well she's eating. That is a surefire way to see if she's getting enough. If her breast bone feels bony with very little meat on it compared to the others then I would be concerned that she's slowly starving. If she's just eaten and you feel that there is barely anything in her crop then that would also be an indication she's not getting enough to eat.
Her cross-beak doesn't look as bad as some I've seen but if you plan to keep her alive you will need to file her beak on a fairly regular basis, at least once a month depending on how fast it grows. Because the front part of her beak doesn't meet together as it should, it will not naturally file down as she pecks like it would on a non handicap chicken. The more it grows without being filed, the harder it will be for her to eat. A large very course finger nail file works well for this. She will also likely never be able to eat food in pellet form but you'll just have to watch and see what type of food she has the best success with. As far as containers, it may be that the 1" hanging feeder is easier for her, in which case you'll always need to make sure food is available in it. I would think the dog feeder would be easier for her, but you'll be the best one to make that decision.
It is my opinion that if you have to force feed her to keep her alive, she's not living a quality life and should be put down. I've force fed a hen before but it was a hen that eventually got better and was able to eat on her own so force feeding was no longer required. As far as I know, this is not a condition that will get better with time.
If you decide that she requires more maintenance than you can handle, don't feel bad about putting her down. It is neither right nor wrong to keep her alive. Animals were put here for us, not the other way around so I would recommend you make a decision your heart can be settled with.