The fact of the matter is there never will be absolute proof of these questions. The naysayers will always have straws to grasp at.
Every time I've been involved in a rewrite, including ones using the same language before/after, the outcome has been good. The act of doing a full rewrite is where the benefit comes from, it's hard to separate that from a language switch.
edit: To clarify this thought a bit, obviously you can transpile code in a type safe language to JavaScript. At the abstraction level of the code written, the project is type safe. The generated JavaScript itself is not; however this isn't a problem if the transpiler is correct. The same principle applies to Haskell compiling to non-typesafe machine code.
So, anyone doing this should consider trying to get a sample of people who are more or less indifferent between the options, so they don't sabotage the test