There are other things on the View Menu like targets Text Zoom, Targets, Toolbar, Status Bar, etc. I think you could just put UI Mode in the same group at Targets and Text Zoom.
Let's leave the button as it is. There is a balance between the uninitiated and those in the know. Once you know where to look, having it on the right makes it highly visible, because it is so separate from the other buttons. I don't really think putting it in with the other buttons is likely to make it more findable.
I guess I wonder a bit whether anything we have discussed so far would have really kept the course participant who chose Mixed from asking me how to change his choice to Proteomics after the fact.
I kind of wonder whether the simplest most direct way to solve that would be to follow the choice form with another form that shows a picture of the toolbar button (with enough context to learn it is on the right side of the toolbar) with a red arrow pointing to it, reminding a user after they make their choice that they can always change with that button.
Not sure the View menu is any more discoverable by the person who quickly decides they want to change their choice but isn't sure how.