I often come across sentences such as, "Our program assists, at no cost, students maintain independent living..." I believe it should be written as, "Our program assists, at no cost, students to maintain independent living..." Input? This isn't a question about the word "help" - this is specifically about the word "assist."
Every example you give is mangled. What you're trying to say, I think, should be said thusly: "Our program assists students in maintaining independent living, at no cost" or "Our free program assists students in maintaining independent living."
Truthfully, it still sounds weird; I would probably re-write the whole thing if I had more of the surrounding text for context. Hope this helps.