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
Right, yes. Perhaps this entire exercise is a complete waste of time. Perhaps we should be investing in skilled people who understand their problem domain and then just trust them to do the best they can, rather than trying to find silver bullets inside programming languages.
What we can do is compare similar types of projects in different languages. And the things we can say there are pretty significant. For instance, at my last job using Angular we experienced a particular bug in production a couple times. In my current job our frontend is written in Haskell. I don't make definitive statements that often, but in this case I can definitively say that there is a ZERO chance that bug will happen in our codebase. I can say that because the type system guarantees that that class of bug can't possibly happen.