Refer them to psych. Some behaviors are inevitable, (I work on a similar floor with 40 alzeheimer's pts), but these resident's are in distress and it's not fair to THEM. I understand about not getting your work done, believe me I have joked "I could do my job so much better without the resident's!", but of course that's silly.
In the best world psych has most behaviors under control with the exact right amount of drugs to keep the resident's comfortable without being snowed. (I hate seeing them snowed). AND, you have a dedicated activities person to keep the higher functioning ones somewhat occupied for some of the time.
Inevitably, you will have hangers on, crying and calling out, wheelchair collisions, falls and many many trips to the bathroom, (for them) in between doing your other work. Because when you work on a floor like that, EVERYTHING is YOUR work. The resident's and their needs are your work. I know we all want to get out on time, and admin may insist you do, but that's unrealistic. Working with these resident's is a lobor of love and some people don't want to do it. It's emotionally and physically draining in a way that other nurses don't understand or don't want to deal with.
And you're right, more staffing IS the answer and it's probably NOT going to happen. IN our facility we are even told "they have the right to fall" WHAT??
So, you do your best. You work with and around them. You help the aides and they help you. AND ask the doc and the psych doc if some of the ones showing anxiety, depression, etc (you have to have a dx they can work with, not just so-and-so is a pita and they follow me all day and night) can have something to take the edge off. Best of luck, you either sink or swim in this business. Some days I'm the bug and sometimes I'm the windshield....oh, and go to bed early, you're gonna need your sleep! :/