Welcome to the JavaRanch, Andrew!
I think you are a prime candidate for a very old but still very useful article from IBM DeveloperWorks. It's a 3-part series by Rick Hightower titled "JSF for non-believers". It pretty much describes your sort of situation and shows simply how to handle it.
This is a very old article, but it still works. The main changes since then is that now you can define beans with annotations as well as with faces-config.xml (faces-config overrides annotations, BTW). And
JSF has added View scope.
Request scope in JSF is almost entirely useless, and especially so in cases where you are maintaining a DataModel object(s).
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.